I towed a trailer once that had the brakes wired to the brake light wire. Stopping and even turning was an adventure.
You can do one of two things, depending on how you want to proceed. First, hook up the brakes, one wheel at a time, and see if one of them shorts your brake controller. Second would be to replace the brakes with complete backing plate assemblies. First option is cheaper, but the second will give you more peace of mind.
Meddle not in the affairs of dragons, for you are crunchy, and taste good with ketchup.