Dave and Kevin. I pulled out my little portable 12V
power supply and found one wire that was not bundled with the others and that was the ground. Putting 12V
across the rest revealed my running, brake and blinker lights. It seems likely that the other "romex" type is the electric brakes (which I'm not using.)
So I'm guessing that the two wires in the other plug are to supply 12V to the trailer from the vehicle. I was planning on installing a battery. Should I attach the battery to that plug? I haven't been able to trace yet where those wires go. But I'll keep trying unravel the electrical tape around this mystery! Thanks for the advice, it's been a real help.