Buddy just got a boat and we were giving it the once over. (oil change, airfilter, greasing the shaft) Hooked it up to a 12v Battery to test the starter. Started just fine, like it always does, ran it for 5 or so minutes then shut it off. As soon as we shut it off it started smoking from both sides. Took the front cowling off and found a black wire running on top of the engine and behind the starter cowling. The wire was obviously burnt up (see the attached pics). I know a bit about small engines but a little confused by this one.

I think it's for the coil? Not positive just hooked up a kill switch on my 35 and the black wire was the coil wire just a guess

After looking around google a little bit more I think that may be it. Any ideas of what could have caused it to short? The magnetos are pretty rusty but we are planning on cleaning them before we take it out. Is that engine able to use 12v without burning it up?

It should, I wouldn't see why not. If I had to guess I'd say over time the rubber coating wore off and caused it too short out. Just from vibration and not being properly secured. I'd just get some wire about the same size preferably a little bigger and hook it back up.