Brake light on when disconnected from the switch is a challenging mystery.
You have to find out where the electrical energy is coming from. It is not possible for the light to be on without electricity from somewhere. Somehow, someway, electricity is getting into the brake light wire.
My guess, strictly a guess, is the wiring bundle at the bottom of the steering column is somehow crossed or shorted. It is the only place I can think of that would supply the current, absent a major mistake. The repo switches are not very good at keeping the connections separated, but even that does not make much sense if the switch is unwired.
Assuming everything else is off, and double check that assumption, one way is to get a pal to watch the light, and start dis-connecting the wire, starting from the wire into the light and go forward, until it goes off. Or, by yourself, trace it with a voltage and continuity tester from the light forward.
I look forward to seeing the solution. Please keep us advised.