Brake pedal draws power stalls car

You have an electrical short in the wire harness somewhere between the brake light switch and the rear lights.
I don't think you were overheating, just that the gauge got more power put into it than it is supposed to have.

There is an electrical connector for the rear lights behind your drivers side kick panel.
If it were my car I would disconnect that and try it again.
I have even seen screws that were too long put in the trim panel along the carpet edges that went into those wires and caused a bunch of mixing of the lighting. (like dash lights coming on when the brakes were applied)