See http://wordpress.stackexchange.com/a/247514/8521

clock-behavior.js

/* global jQuery, wp */
jQuery( function( $ ) {

	var initializeAllClocks, initializeClock;

	/**
	 * Find clocks.
	 *
	 * @param [container] Scoping element for finding clock elements.
	 * @returns {void}
	 */
	initializeAllClocks = function( container ) {
		$( container || document.body ).find( '.wpse-247251-clock' ).each( function() {
			initializeClock( $( this ) );
		} );
	};

	/**
	 * Initialize clock.
	 *
	 * @param {jQuery} clockElement Clock element.
	 * @returns {void}
	 */
	initializeClock = function( clockElement ) {
		var timeoutId, populateTime;

		if ( clockElement.data( 'initialized' ) ) {
			return;
		}

		populateTime = function() {
			clockElement.text( new Date().toString() );
		};

		timeoutId = setInterval( function() {

			// Stop interval when element is no longer in the DOM.
			if ( ! $.contains( document, clockElement[0] ) ) {
				clearInterval( timeoutId );
				return;
			}

			populateTime();
		}, 1000 );

		populateTime();
		clockElement.data( 'initialized', true );
	};

	initializeAllClocks();

	// Re-initialize clocks when a partial is updated in the customizer preview.
	if ( 'undefined' !== typeof wp && 'undefined' !== typeof wp.customize && 'undefined' !== typeof wp.customize.selectiveRefresh ) {
		wp.customize.selectiveRefresh.bind( 'partial-content-rendered', function( placement ) {
			initializeAllClocks( $( placement.container ) );
		} );
	}
} );

color-scheme-dark.css

.widget.color-scheme-dark,
.widget.color-scheme-dark h2,
.widget.color-scheme-dark p {
	color: white !important;
	background: navy !important;
}

color-scheme-light.css

.widget.color-scheme-light,
.widget.color-scheme-light h2,
.widget.color-scheme-light p {
	color: black !important;
	background: palevioletred !important;
}

countdown-behavior.js

/* global jQuery, wp */
jQuery( function( $ ) {

	var initializeAllCountdowns, initializeCountdown;

	/**
	 * Find countdowns.
	 *
	 * @param [container] Scoping element for finding countdown elements.
	 * @returns {void}
	 */
	initializeAllCountdowns = function( container ) {
		$( container || document.body ).find( '.wpse-247251-countdown' ).each( function() {
			initializeCountdown( $( this ) );
		} );
	};

	/**
	 * Initialize countdown.
	 *
	 * @param {jQuery} countdownElement Countdown element.
	 * @returns {void}
	 */
	initializeCountdown = function( countdownElement ) {
		var timeoutId, populateCountdown;

		if ( countdownElement.data( 'initialized' ) ) {
			return;
		}

		populateCountdown = function() {
			var now, newYearDate;
			now = new Date();
			newYearDate = new Date( now.getFullYear() + 1, 0, 1, 0, 0, 0 );
			countdownElement.text( 'T-' + String( Math.floor( ( newYearDate.valueOf() - now.valueOf() ) / 1000 ) ) );
		};

		timeoutId = setInterval( function() {

			// Stop interval when element is no longer in the DOM.
			if ( ! $.contains( document, countdownElement[0] ) ) {
				clearInterval( timeoutId );
				return;
			}

			populateCountdown();
		}, 1000 );

		populateCountdown();
		countdownElement.data( 'initialized', true );
	};

	initializeAllCountdowns();

	// Re-initialize countdowns when a partial is updated in the customizer preview.
	if ( 'undefined' !== typeof wp && 'undefined' !== typeof wp.customize && 'undefined' !== typeof wp.customize.selectiveRefresh ) {
		wp.customize.selectiveRefresh.bind( 'partial-content-rendered', function( placement ) {
			initializeAllCountdowns( $( placement.container ) );
		} );
	}
} );

customize-preview.js

/* global wp, _ */
/* exported WPSE_247251 */
var WPSE_247251 = (function( api ) {

	var component = {
		data: {
			enqueued_styles: {},
			enqueued_scripts: {}
		}
	};

	/**
	 * Init.
	 *
	 * @param {object} data Data exported from PHP.
	 * @returns {void}
	 */
	component.init = function init( data ) {
		if ( data ) {
			_.extend( component.data, data );
		}
		api.selectiveRefresh.bind( 'render-partials-response', component.handleRenderPartialsResponse );
	};

	/**
	 * Handle render-partials-response event, requesting full refresh if newly-enqueued styles/styles differ.
	 *
	 * @param {object} response Response.
	 * @returns {void}
	 */
	component.handleRenderPartialsResponse = function handleRenderPartialsResponse( response ) {
		if ( ! response.wpse_247251 ) {
			return;
		}
		if ( ! _.isEqual( component.data.enqueued_styles, response.wpse_247251.enqueued_styles ) ) {
			api.selectiveRefresh.requestFullRefresh();
		}
		if ( ! _.isEqual( component.data.enqueued_scripts, response.wpse_247251.enqueued_scripts ) ) {
			api.selectiveRefresh.requestFullRefresh();
		}
	};

	return component;
})( wp.customize );

wpse-247251.php

<?php
/**
 * Plugin Name: WPSE 247251: Initiating Full Refresh when Selective Refresh Enqueues Different Styles
 * Author: Weston Ruter, XWP
 * Author URI: https://make.xwp.co/
 * Plugin URI: http://wordpress.stackexchange.com/questions/247251/how-to-mix-partial-and-full-page-refresh-in-the-same-section-of-the-customizer
 *
 * Copyright (c) 2016 XWP (https://make.xwp.co/)
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License, version 2 or, at
 * your discretion, any later version, as published by the Free
 * Software Foundation.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
 *
 * @package WPSE_247251
 */

namespace WPSE_247251;

/**
 * Class Plugin
 */
class Plugin {

	/**
	 * Example widget.
	 *
	 * @var Example_Widget
	 */
	public $widget;

	/**
	 * Plugin registered style handles.
	 *
	 * @var array
	 */
	public $registered_style_handles = array();

	/**
	 * Plugin registered script handles.
	 *
	 * @var array
	 */
	public $registered_script_handles = array();

	/**
	 * Add hooks.
	 */
	function add_hooks() {
		add_action( 'widgets_init', array( $this, 'register_widget' ) );
		add_action( 'wp_enqueue_scripts', array( $this, 'enqueue_dependencies' ) );
		add_action( 'customize_render_partials_before', array( $this, 'enqueue_selective_refresh_dependencies' ), 100 );
		add_filter( 'customize_render_partials_response', array( $this, 'filter_customize_render_partials_response' ) );
	}

	/**
	 * Register widget.
	 */
	function register_widget() {
		$this->widget = new Example_Widget();
		register_widget( $this->widget );
	}

	/**
	 * Enqueue dependencies.
	 */
	function enqueue_dependencies() {
		$light_color_scheme_style_handle = 'wpse-247251-color-scheme-light';
		$src = plugin_dir_url( __FILE__ ) . 'color-scheme-light.css';
		wp_register_style( $light_color_scheme_style_handle, $src );

		$dark_color_scheme_style_handle = 'wpse-247251-color-scheme-dark';
		$src = plugin_dir_url( __FILE__ ) . 'color-scheme-dark.css';
		wp_register_style( $dark_color_scheme_style_handle, $src );

		$clock_behavior_script_handle = 'wpse-247251-clock-behavior';
		$src = plugin_dir_url( __FILE__ ) . 'clock-behavior.js';
		$deps = array( 'jquery' );
		if ( is_customize_preview() ) {
			$deps[] = 'customize-selective-refresh';
		}
		wp_register_script( $clock_behavior_script_handle, $src, $deps );

		$countdown_behavior_script_handle = 'wpse-247251-countdown-behavior';
		$src = plugin_dir_url( __FILE__ ) . 'countdown-behavior.js';
		$deps = array( 'jquery' );
		if ( is_customize_preview() ) {
			$deps[] = 'customize-selective-refresh';
		}
		wp_register_script( $countdown_behavior_script_handle, $src, $deps );

		$this->registered_style_handles = array( $light_color_scheme_style_handle, $dark_color_scheme_style_handle );
		$this->registered_script_handles = array( $clock_behavior_script_handle, $countdown_behavior_script_handle );

		// Enqueue dependencies only if they are used by widgets.
		$instances = $this->widget->get_settings();
		foreach ( wp_get_sidebars_widgets() as $sidebar => $sidebar_widgets ) {
			foreach ( $sidebar_widgets as $widget_id ) {
				if ( ! preg_match( '/^' . Example_Widget::ID_BASE . '-(?P<number>\d+)$/', $widget_id, $matches ) ) {
					continue;
				}
				if ( ! isset( $instances[ $matches['number'] ] ) ) {
					continue;
				}
				$instance = array_merge( $this->widget->default_instance, $instances[ $matches['number'] ] );
				if ( 'light' === $instance['color_scheme'] ) {
					wp_enqueue_style( $light_color_scheme_style_handle );
				} elseif ( 'dark' === $instance['color_scheme'] ) {
					wp_enqueue_style( $dark_color_scheme_style_handle );
				}
				if ( 'clock' === $instance['behavior'] ) {
					wp_enqueue_script( $clock_behavior_script_handle );
				} elseif ( 'countdown' === $instance['behavior'] ) {
					wp_enqueue_script( $countdown_behavior_script_handle );
				}
			}
		}

		// Enqueue helper script for listening to selective refresh events.
		if ( is_customize_preview() ) {
			$preview_handle = 'wpse-247251-customize-preview';
			$src = plugin_dir_url( __FILE__ ) . 'customize-preview.js';
			$deps = array( 'customize-selective-refresh' );
			wp_enqueue_script( $preview_handle, $src, $deps );

			// Export which widget styles specifically where enqueued.
			wp_add_inline_script(
				$preview_handle,
				sprintf( 'WPSE_247251.init( %s )', wp_json_encode( $this->get_enqueued_dependencies() ) ),
				'after'
			);
		}
	}

	/**
	 * Get enqueued dependencies.
	 *
	 * @return array Enqueued dependencies.
	 */
	public function get_enqueued_dependencies() {
		$data = array(
			'enqueued_styles' => array(),
			'enqueued_scripts' => array(),
		);
		foreach ( $this->registered_style_handles as $style_handle ) {
			if ( wp_style_is( $style_handle, 'enqueued' ) ) {
				$data['enqueued_styles'][ $style_handle ] = true;
			}
		}
		foreach ( $this->registered_script_handles as $script_handle ) {
			if ( wp_script_is( $script_handle, 'enqueued' ) ) {
				$data['enqueued_styles'][ $script_handle ] = true;
			}
		}
		return $data;
	}

	/**
	 * Enqueue scripts in selective refresh responses.
	 *
	 * Core should do this eventually, hence the conditional. See core docs
	 * for the `customize_render_partials_before` action.
	 */
	function enqueue_selective_refresh_dependencies() {
		if ( ! did_action( 'wp_enqueue_scripts' ) ) {
			wp_enqueue_scripts();
		}
	}

	/**
	 * Export the enqueued styles in the selective refresh response.
	 *
	 * Note that core should eventually include the enqueued scripts/styles by
	 * default. See docs for the `customize_render_partials_response` filter.
	 *
	 * @param array $response Response.
	 * @return array Response.
	 */
	function filter_customize_render_partials_response( $response ) {
		$response['wpse_247251'] = $this->get_enqueued_dependencies();
		return $response;
	}
}

/**
 * Class Example_Widget
 */
class Example_Widget extends \WP_Widget {

	const ID_BASE = 'wpse_247251';

	/**
	 * Default instance.
	 *
	 * @var array
	 */
	public $default_instance;

	/**
	 * Sets up a new widget instance.
	 */
	public function __construct() {
		$widget_ops = array(
			'classname' => 'widget_wpse_247251',
			'description' => __( 'WPSE 247251', 'wpse-247251' ),
			'customize_selective_refresh' => true,
		);
		$this->default_instance = array(
			'title' => '',
			'color_scheme' => 'light',
			'behavior' => 'clock',
		);
		parent::__construct( self::ID_BASE, __( 'WPSE 247251', 'wpse-247251' ), $widget_ops );
	}

	/**
	 * Outputs the content for the current widget.
	 *
	 * @param array $args     Display arguments including 'before_title', 'after_title', 'before_widget', and 'after_widget'.
	 * @param array $instance Settings for the current Text widget instance.
	 */
	public function widget( $args, $instance ) {
		$instance = wp_parse_args( (array) $instance, $this->default_instance );
		if ( empty( $instance['title'] ) ) {
			$instance['title'] = __( 'WPSE Example', 'wpse-247251' );
		}

		/** This filter is documented in wp-includes/widgets/class-wp-widget-pages.php */
		$title = apply_filters( 'widget_title', empty( $instance['title'] ) ? '' : $instance['title'], $instance, $this->id_base );

		$args['before_widget'] = preg_replace(
			'/(?<=class=")/',
			esc_attr( 'color-scheme-' . $instance['color_scheme'] . ' ' ),
			$args['before_widget'],
			1
		);

		echo $args['before_widget'];
		printf( '<div class="color-scheme-%s">', esc_attr( $instance['color_scheme'] ) );
		echo $args['before_title'] . $title . $args['after_title'];
		echo '<p>' . esc_html__( 'This widget demonstrates how full refresh can be invoked when selective refresh returns with different scripts or styles being enqueued.', 'wpse-247251' ) . '</p>';
		if ( 'clock' === $instance['behavior'] ) {
			echo '<p>' . esc_html__( 'Clock: ', 'wpse-247251' ) . '<span class="wpse-247251-clock">' . esc_html__( 'Loading...', 'wpse-247251' ) . '</span></p>';
		} elseif ( 'countdown' === $instance['behavior'] ) {
			echo '<p>' . esc_html__( 'New Year Countdown: ', 'wpse-247251' ) . '<span class="wpse-247251-countdown">' . esc_html__( 'Loading...', 'wpse-247251' ) . '</span> ' . esc_html__( '(seconds)', 'wpse-247251' ) . '</p>';
		}
		echo $args['after_widget'];
	}

	/**
	 * Handles updating settings.
	 *
	 * @param array $new_instance New settings for this instance.
	 * @param array $old_instance Old settings for this instance.
	 * @return array Instance.
	 */
	public function update( $new_instance, $old_instance ) {
		$instance = $old_instance;
		$instance['title'] = sanitize_text_field( $new_instance['title'] );
		if ( in_array( $new_instance['color_scheme'], array( 'light', 'dark' ), true ) ) {
			$instance['color_scheme'] = $new_instance['color_scheme'];
		}
		if ( in_array( $new_instance['behavior'], array( 'clock', 'countdown' ), true ) ) {
			$instance['behavior'] = $new_instance['behavior'];
		}
		return $instance;
	}

	/**
	 * Form.
	 *
	 * @param array $instance Instance.
	 * @returns void
	 */
	function form( $instance ) {
		$instance = wp_parse_args( (array) $instance, $this->default_instance );
		$color_scheme_options = array(
			'light' => __( 'Light', 'wpse-247251' ),
			'dark' => __( 'Dark', 'wpse-247251' ),
		);
		$behavior_options = array(
			'clock' => __( 'Clock', 'wpse-247251' ),
			'countdown' => __( 'Countdown', 'wpse-247251' ),
		);
		?>
		<p>
			<label for="<?php echo $this->get_field_id( 'title' ); ?>"><?php esc_html_e( 'Title:', 'wpse-247251' ); ?></label>
			<input class="widefat" id="<?php echo $this->get_field_id( 'title' ); ?>" name="<?php echo $this->get_field_name( 'title' ); ?>" type="text" value="<?php echo esc_attr( $instance['title'] ); ?>"/>
		</p>

		<p>
			<label for="<?php echo $this->get_field_id( 'color_scheme' ); ?>"><?php esc_html_e( 'Color Scheme:', 'wpse-247251' ); ?></label>
			<select id="<?php echo $this->get_field_id( 'color_scheme' ); ?>" name="<?php echo $this->get_field_name( 'color_scheme' ); ?>">
				<?php foreach ( $color_scheme_options as $value => $text ) : ?>
					<option value="<?php echo esc_attr( $value ); ?>" <?php selected( $instance['color_scheme'], $value ) ?>><?php echo esc_html( $text ); ?></option>
				<?php endforeach; ?>
			</select>
		</p>

		<p>
			<label for="<?php echo $this->get_field_id( 'behavior' ); ?>"><?php esc_html_e( 'Behavior:', 'wpse-247251' ); ?></label>
			<select id="<?php echo $this->get_field_id( 'behavior' ); ?>" name="<?php echo $this->get_field_name( 'behavior' ); ?>">
				<?php foreach ( $behavior_options as $value => $text ) : ?>
					<option value="<?php echo esc_attr( $value ); ?>" <?php selected( $instance['behavior'], $value ) ?>><?php echo esc_html( $text ); ?></option>
				<?php endforeach; ?>
			</select>
		</p>
		<?php
	}
}

$wpse_247251_plugin = new Plugin();
add_action( 'plugins_loaded', array( $wpse_247251_plugin, 'add_hooks' ) );