I might start by checking the ground wire of the taillight assembly. Make sure there isn't any rust that is preventing a good electrical connection to the chassis ground.
if i read that right lol all cars do that that is just the way they are set up if ur lights arent on your brake light dont need to be on hell as long as someone sees your reverse lights ur fine but anyways all cars do that
Possible ground issue at the taillights.
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.
You probably have a loose wire connection in the brake light sockets. Insert a nail or probe tip into the back of the light socket where the wires are inserted and test the brake lights. (The socket can appear perfectly normal and the wires may even seem well attached.)
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.
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.
head lights
Most likely a fuse.