@PaulS I was hoping to do it without modifying the circuit. My switch in currently a little lever back and forth. It is too stiff for a servo to move, but I could get a different switch. I have a good grasp on how to control motors with an arduino, so this may be a good option for my lack of electronics expertise.
@LarryD I am sorry, but I am not sure what you mean by load. The circuit is driven by a 12V function generator. It carries 1-700mA depending on the moment. Is that the information you need?
I am currently using a switch. After googling relay I think I understand that I can give it a little voltage (like the 5V an arduino can supply) and it will turn on a larger circuit (like my 12V one). (I found this website the easiest to understand http://www.explainthatstuff.com/howrelayswork.html). I am nervous because online it seems like relays can hurt the arduino. I keep seeing that people connect them to transistors. Do I have to do this? Or can I directly put a relay in where the switch is?
Thank you all so much for your help! I am new to electronics, but am trying to learn. Your help is teaching me so much!