Ya your brake switch is fine. Do you have a coupe or sedan the coupe has 4 brake lights 2 inner and 2 outer. The sedan only has 2 lights. Any way thy are 3 wire going to any brake light one will have 12 volts with the brake pedal pressed, one will have 12 volts with the headlights turned on one is the ground it will have next to 0 volts. You said yourself It seems no effect whether brake pedal is down or not and your taillights work fine this means your ground is fine. Your brake switch is working but power is not getting to the other brake lights end of story. You have an open wire between your brake switch and your brake lights or your dumb brake light failure senser has failed lol.

I think it is the brake light failure senser it runs power to the brake lights but not the high mount on the coupe or sedan. Its a little gay black box with 5 wires running to it coupe or sedan its in your trunk next to the brake lights.