Thanks for all the replies guys. It turns out you are all correct. I'm not a doctor but I play electrical engineer at work.
It depends on many things but chiefly: length, temperature rise, and acceptable voltage drop. In this case since it's not going to be operated for very long you can also throw in duty cycle.
18 gauge would do it but with little margin in my mind. Almost 2 watts dissipated in the wire itself. So something larger than that. It would mostly likely come down to what connectors will fit nicely.
I will post pictures of course as well as a bill of materials when I'm done. Don't hold your breath though. I gotta wait until I actually have the tractor back.