Push Button automation

Hello, apologies if i have posted in the wrong thread  but i need some help.. I managed to dismantle a plush toy (with moving parts) which i am going to incorporate in my project. The only problem is that it has a push button so in order to activate the cycle (moving arms) you have to push the button and after a few seconds it stops. If you push the button before it stops it stops. As such, there appears to be some sort of microcontroller which stops the cycle. I'm a newbie to all this electronic stuff but is there another way to incorporate another switch where the cycle continues without the need to push the switch again?