Hello,
From the video, I can’t tell very well, but this looks a lot like the shifting system on a bicycle. Here is a forum post about someone working out some of the details for making an electronic bicycle shifter:
https://forum.pololu.com/t/newbie-in-need-of-advice-about-servo-controlling/1782/1
If you want to power it off the 12V battery, you will need a voltage regulator (probably a linear regulator) that can regulate the voltage down to servo voltage level (4 to 6 volts depending on the servo) and can deliver enough power to actuate the servo.
This project looks like it could be pretty dangerous. Do you have plans for some kind of safety override if the electronics fail?
- Ryan