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.
Possible ground issue at the taillights.
if you recenly replaced bulbs u may have installed them backwards they should be running lights and brake lights if this is the case they maybe installed incorrectly
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.
are you sure it is the brake lights and not the tail lights. if it is the brake lights you most likely have a short some where. go to a auto eletrican It is the brake lights which turn on. Short in the switch or the wiring?
The brake lights should not come one until you step on the brakes. The tail lights should come on when the headlights are on. If they're weak, maybe there's dirt in/on the lenses or maybe the bulb is old and clouded. Change the bulbs and see if that improves things.
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.
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.