its probably old a brittle from age. id suggest going down to an auto parts store like napa, and getting a new harness, they are cheap typically under $20. then just tracking your wires back to the control box probably in behind one of the interior side panels by the tails lights, splice into that on the far side/trailer side of the box -give your self like 8-12" of lead before splicing, and splice the wires at different lengths, like at increasing 2" increments (so you dont end up with a big bulging section of butt connectors ect) and then you will have all new wires running to your plug.
i say leave the 8-12" so that you still have wire to do this again at a later time if something else happens, but its close enough that all of your new connections should still be inside the vehicle. and out of the elements. wrap the new wires in a loom and call it a day. i did this exact project a few months back. worked like a charm -i used about 6' or so of 3/8" loom and then for the loom that is outside and under the vehicle i over wrapped the 3/8" loom with 1/2" loom and then some silicon self sticking electrical tape. to help keep it on place. no issues or worries of it ever rubbing through to being pinched ect.