As I learned even though the P3 is indicating a short, you still have brakes its just that one of the magnets, or wiring to it has an issue.
What an OP suggested to me and I did was jack up one wheel at a time and spin it, then have someone depress the brake, to locate the wheel. Once that is done and you find the wheel, check the wiring, looking for loose, worn rubbed. You can do a continuity check by connecting both sides to an ohm meter. I bought 50' roll of two conductor 16 gauge wire from the home center (lamp cord) and soldered on alligator clips. I stuck it in the appropriate hole on the 7 way plug then back to the wheel.
In my case the wires were fine, trailer ground was fine, and it turned out to be the magnet. The OP said if the wires are good just replace the magnet and that's what I did. Problem solved. I now always carry two sets of full brake assemblies with me as my brake problem occur hundreds of miles from home. I also carry wire. Never a good feeling being over the road with a problem. I hope that this helps you.
Happy trails