First you need to understand that most, if not all, vehicle [autos, trucks, and trailers] rear lighting systems have both tail light bulbs and brake light bulbs, OR a single bulb on each side [right and left] that each have two filaments [what glows when electricity is applied]. The tail lights are supposed to be on when the headlights, or parking lights, in the towing vehicle are turned on. The separate brake light bulb, or brake light filament in the dual filament bulbs is only supposed to turn on when the brake pedal is depressed, and the towing vehicle brake lights are on. I suspect that what you are calling brake lights are actually the tail lights. To check this out, run some tests. Have an assistant sit in the vehicle and do the following on your command: 1. Apply brakes by pressing on the brake pedal. The brake lights should turn on. 2. With foot OFF of the brake, turn on the headlights. The trailer tail lights should turn on. 3. With the headlights on, have the assistant depress the break pedal. Even though the tail lights are already on, the brake lights should come on also, causing the trailer lights to brighten noticeably 4. While you're checking, have the assistant turn the ignition key to on, and one at a time test the left and right turn signals. Again, I think what you think are brake lights, are actually the tail ligts.
the brake lights are on a separate cuircut,if your brake lights are staying then it will be a fault with the brake light switch. the switch is located under dash,and will be on or very close to brake pedal.
Possible ground issue at the taillights.
that sounds like i ground in the bake by the lights or if it has a trailer plug i would start their
they are not brake lights they are fog lights and they turn on because it is for the car behind to see you
Check the fuse for the headlights. It is probably open.
Fuse for parking lights probably blown.
Often this type of behavior is caused by a bad ground for the lighting circuit. Check the ground circuit for the brake lights.
ummm... your brake lights should ALWAYS work whether your headlights are on or not, that's how people behind you know you are stopping.
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.
head lights
Most likely a fuse.
The brake lights and the tail lights are separate circuits. Check the brake light fuse, then check the brake light bulbs, then check the brake light switch.