Third brake light

Hi everyone, I have a 2000 Ford Mustang. Right once you turn the ignition on the third brake light lights up barely and will always stay on. When you turn the headlights on the brake lights are always on. I’ve checked the bulbs, brake light switch, headlight switch, pulled fuses and the only fuse that made it go off was #41 and it’s for the brake lamp. This all started when I connected the battery again after a motor swap. Also the battery was disconnected for 8 months. During the motor swap the only wiring I touched was in the engine bay. What could this possibly be? Also the car has a remote starter and it doesn’t work because the remote starter thinks someone is always pressing the brake when the ignition goes on. Brought the car back to where the alarm was put in and they said it isn’t caused by the alarm. This started before I put leds in the car.
 
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this is what it always looks like with ignition on, when the turn signal is on it gets brighter then it will dim down when it goes off. Have power at brake switch and it is working.
 
LED's require very little voltage to actually run. Theres a few circuits that run through the brake light circuit to check integrity (cruise control) so they create a little current draw. I'd have to check wiring diagrams to confirm this fully. LED brake lights messes with this.

What lights do you have for the standard taillights? LED bulbs as well? When you had stock bulbs, they still glowed dimly? Any wiring mods that you know of elsewhere in the car.