What does Button Rhythm actually do?

In yew's words: "Button rhythm is turning your regular button shot into a rhythm shot. When you press Square, your controller's right stick gets pulled down (on the software output level, not in real life) and this starts a rhythm shot — then when you release the button, it smoothly flicks the stick up to give it rhythm."

You still press and release the button yourself. The script only changes what the console sees from the right stick during that press. The result is a bigger green window, a smaller shot-contest penalty and more consistent releases — not automatic timing.

Source: yew's published settings.