Brake lights draw their energy from the vehicle's battery.
Defective battery or something is pulling power from the battery. Check the glove box light, interior lights, trunk light, hood light, brake lights, etc.
the connection between the battery and the brake lights
I have a 03 gran prix and my brake lights doesn't come on when I go to brake
You probably have a bad ground. Check the grounds on the brake lights.
Do you mean What does it mean when the brake and battery lights come on in when it is already started? Check your alternator may be its not working well it cause the battery sign comes out.
Bad brake switch. Typically located at the top of the brake pedal.
"Stuck" brake lights indicate that the brake light switch on the brake pedal is broken. It should be replaced.
Battery dead
I would suspect the brake light switch is broken or out of adjustment. The switch is located just above the brake pedal pad. or i think that brake is stuck??
The BOO (Brake On/Off) Switch may need to be replaced. If it is bad, it would cause the brake lights to NOT illuminate when the brake pedal is applied.
Either the battery has a dead cell and needs replacing, or alternator is defective, loose or corroded battery cables, or something is draining the battery. Look for a courtesy, trunk, under hood, glove box light that is on. Also can be a defective brake light switch which causes the brake lights to stay on.