It's not a bench hook. https://en.wikipedia.org/wiki/Bench_hook
It's not a style of bench.
It's a wood working jig/guide.
https://archive.org/embed/letsmakelotofthi00zarc page 48
https://archive.org/details/letsmakelotofthi00zarc/page/48/mode/2up?q=%22bench+fork%22
Cut a triangular notch out of the center of one of the short sides of a 8"x4" board.
Now you can clamp this piece on a larger bench, and use the cutout area while using a Coping Saw.
https://en.wikipedia.org/wiki/Coping_saw!
