Break lights come on when you step on the break, they do not come on when the head lights are turned on.
The parking brake light stay lit on the 1999 Mitsubishi Montero sport the parking brake is working and you have not put the light off.
The 1995 Mitsubishi flasher relay switch and the brake light relay switch can be found beneath the dashboard. Both switches will be on the drivers side of the dashboard, near the brake pedal.
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.
Remove the tire and wheel from your 1997 Mitsubishi Montero. Remove the brake shoe assembly. Tap on the rotors to loosen them. The rotors will slide off. Reverse the process to install your new rotors.
Often this type of behavior is caused by a bad ground for the lighting circuit. Check the ground circuit for the brake lights.
Fuse for parking lights probably blown.
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.
check your clutch and brake fluid