This is usually a grounding problem. Either an insufficient ground to the assy or a positive to ground problem. As you mention the brake lights work with the lights off, it will probably be related to a problem with the "running lights" system. As you mention only a problem with the passenger rear, I would check for a poor ground related to that light assy or possibly one of the bulbs' internal filaments in that assy touching each other. Or possibly a socket failure at that assy. Good Luck
Brake lights should NOT be effected by the headlights. Brake light function is completely independent of the headlights. Assuming you are not refering to the tail lights, or marker lights, which are supposed to come when the head lights are turned on. Not having brake lights when the head lights are on is a big safety problem and should be corrected.
Check the ground wire to the brake lights.
They Do
yes, they do
Assuming you have the lights turned off, you are seeing the brake lights. They are more than likely on because the brake light switch is defective or out of adjustment.
On a toyota tacoma 2003 SR5 when the tail lights are turned on the brake lights come on and when the tail lights are of the brake lights work just fine what could be the problem. If the truck has a trailer plug, inspect the plug and plug wiring for damage and corrosion.
Bulbs blown/Brake lamp switch inoperative
Answerwire shortage!Brake light switch is broken or out of adjustment.
Check bulbs Check fuse for parking/tailights Check brake light fuse
Break lights come on when you step on the break, they do not come on when the head lights are turned on.
check and/or replace brake pedal switch.
the parking brake may be stuck and that causes the brakes to lock up completely, and the horn and lights will stick work if the parking brake is stuck.