Can anyone offer an explanation of the 2nd wire connected to the negative house battery post? I cannot find where the other end terminates. I was guessing it's the battery temperature monitor albeit not marked so; and furthermore the configuration of the connecter doesn't look like anything more than a 4 wire phone cable. The Red and Green wires are buried in some epoxy in the terminal end; the Yellow and Black wires are cut. I've added photos here; How would this serve as a battery temperature sensor?
That would be my first "GUESS" as well.
Go to the inverter/charger and see if those same two wires are on the plug end at the inverter/charger.