Check the brake light switch. Had this happen to me years ago with brake lights staying on.
If you have the push-in style brake light switch, the switch plunger could be loose and not retracting back because the weight of the brake bracket is resting on it causing the switch to keep activating the lights.
I fixed this by using a heavy duty switch that is adjustable. When the switch is installed it can be screwed in and out in the mounting bracket bringing the switch closer or further away from the from the brake bracket. In my case, I rotated out the switch making it further away from the bracket which solved the problem.