Add a Checkbox field to the WordPress Customizer.

WP Customizer - Checkbox

$wp_customize->add_setting( 'themecheck_checkbox_setting_id', array(
  'capability' => 'edit_theme_options',
  'sanitize_callback' => 'themeslug_sanitize_checkbox',
) );

$wp_customize->add_control( 'themeslug_checkbox_setting_id', array(
  'type' => 'checkbox',
  'section' => 'custom_section', // Add a default or your own section
  'label' => __( 'Custom Checkbox' ),
  'description' => __( 'This is a custom checkbox input.' ),
) );

function themeslug_sanitize_checkbox( $checked ) {
  // Boolean check.
  return ( ( isset( $checked ) && true == $checked ) ? true : false );
}