I'll look around... But that has been a subject previously discussed... maybe not this exact thing but close....
The remote picture is tough to tell... but the plug with the wires out of it.... and the switch itself are two different wires yes? With the switch having a plug that goes into the plug that has the flap on it.... (which is the other end of wire missing those wires in the 3 prong plug) because I think that 3 prong plug will looking for a wire bundle with that same plug (reversed ofcourse) I would start my tracing from the winch itself.
I think the info on this may be in a question about wireless winch remotes.... but same info you are looking for...
Another reason, I HATE WIRING!!!! Well, when I didn't start it from the beginning.... lol
Joe