Believe it or not, I have seen this when the wrong bulb is used-or the correct bulb has been forced into the plug backwards. If the wiring has been repaired (look for tape, or connectors) it may have been done correctly. Sometimes there may be a grounding problem also. These lights (rear) will also fill with water, which can cause shorting. If this is the problem, drill a small hole in the bottom of the housing to drain any water (do not reseal it). I had bad grounds on both tail light sockets and back up lights. When ever strange electrical problems happen such as dim lighting, other bulbs lighting that are not suppose to and intermittent turn signal problems, check the ground by using a jumper wire from the grounded part of the socket to a known good ground. If it works fine then it is a bad ground. I soldered the ground wire to the outside of the metal socket. Worked fine.
Possible ground issue at the taillights.
See sources and related links below for 1993 Dodge Shadow tail light, brake light and turn signal light bulb part numbers.
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.
The Dodge Shadow stopped production in 1994
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
replace the headlight switch its wore out replace the headlight switch its wore out