This isn't brain surgery..
Make your life simpler and just scrap the existing brake wire run from front to the axles and be done with it. The factory often uses too light of wire to start with and it is not worth the hassle to attempt to find the intermittent short in it.
Replace the existing wire by upgrading the wire ga 12Ga minimum but larger can often make a huge improvement in your brakes, your brakes will work better than new.
You do not need to find and remove the OEM wire, just cut it out on both ends then run the new wire along the trailer frame.
While doing that pull each brake drum and inspect the magnet wires, they often get tangled inside the drums with the mechanical arms and damage the insulation which can cause intermittent overloads.