If your brake light is on all the time, it might be the plastic grommet on the pedal lever that lets the sensor know you have engaged the brakes. Those dry out over time and will crumble to to the ground in pieces. If you find a small pieces of clearish green rubber, than that is what it is. It happened to my 98' and also happened to my 91' 300zx.
If you have a trailer light harness, check there first. Any other aftermarket wiring work is a good place to check as well. If you don't find issues with either of those areas, I would remove each bulb and check to see if there's an issue with a bulb shorting internally.
yeah you have aftermarket wiring thats fubar. IE a LEd bar trying to bridge the running and brake lights together so the brake will work on the LED. will not work. causes you 3rd brake to be on and brake lights illuminated half assed.
just looked into this last night. haha. I'm a little slow. Been really busy lately. Turned out to be problem in aftermarket trailer wiring. Someone wired the brake light into the ground, so when i hit the brakes it actually caused it to get even brighter. the only reason i actually looked into it was because i wanted to check to see if the wiring harness was working correctly and for some reason all prongs except ground were getting power with just parking lights on. Then i noticed that the white wire was grounded? haha. Then i felt the ground wire connection and it was burning hot. Theres an indication!