Old brakes, Old trailer

Please ignore me if you don't feel this is helpful. Your tow vehicle is ... antiquated. To approach modern safety levels you need great trailer brakes. If it was me (and I know it is not), I'd buy new brake assemblies with drums and bearings. Then I'd run new wires from the new assemblies all the way to the 7 way. The cycle of bad wiring, bad magnets, bad grounds, and rusty parts needs to be cut off at the pass.

Now, some advice you might use. The controller behavior and the brake operation you described indicates bad wiring. The some oxidization that rusted all that stuff probably oxidized the wiring too. It starts at the connections and spreads down the copper turning it black.