How to make a push button toy always on?

I'm modifying toys I've found at thrift stores. I want to be able to flip the on switch and have the toy move until I turn it off. Unfortunately 90% of these toys only work when you turn them on and then press a button to see them dance or go through various motions. I've tried connecting the two wires that go into the button but it only plays through the motion once and then stops.

My idea right now is to attach the wires to a timer so they are activated every 60 seconds or so. Does anyone know how to make a timer like that? Arduino could work but I'd rather do something easier and cheaper.

I attached images of the button that activates the toy. Im hoping to find something that I can just connect to those wires as most of these toys use the same button.

Thank you so much for any help!

You don't even need an arduiono to do that. A 555 IC, capacitor, resistor, and a transistor (in place of switch) will make it repeat at an interval chosen by your RC network. Look up the 555.

Perfect! This is exactly the kind of answer I need. Any idea where I can find info on how to put these pieces together for my desired effect?

Thank you so much@!

Second schematic here:- https://www.electronics-tutorials.ws/waveforms/555_oscillator.html