Wow, they stay on even after you disconnect the brake light switch? Maybe my story will help you somehow....
I'm having similar trouble, but am hoping a new switch will fix it. My ABS light came on a few weeks ago, which I've been ignoring, as I'm hardly driving since covid came and want to avoid another trip to the dealer. Yesterday, my brake lights came on while the car was parked in the carport. If I open a door, pump the brakes, or do just about anything, they will go off... for a while - 15 minutes or a couple of hours. I have an Energi, so this morning I took a drive with the gas engine to charge the (new) 12-volt battery. The little wrench icon appeared, and disappeared, and appeared again. I think it's off again, now! Three thousand youtube videos later, I took another drive to test my cruise control, which (aha!) was not working! Youtube informs me this combo of events means my switch is faulty, as it also controls the on/off of the cruise control. The Auto Parts fellow convinced me to try replacing the cheap brake pedal stop pad first (to save a few bucks, as the switch is not returnable), but I have yet to figure out where it might go - my car's pedal/switch configuration looks quite different than those in the videos (Focus, Fiesta, etc.). So now I'm just going to buy the ~$30 switch, replace my original, and see what happens.
All suggestions are welcome!