The most common cause of a trailer light not working only when the headlights are on and the brake is depressed is a poor ground connection between the vehicle and the trailer. When the headlights are turned on, the additional electrical load can cause a voltage drop in the circuit, which can prevent the trailer lights from receiving enough power to illuminate. When the brake is depressed, the brake lights (which draw more current than the taillights) are also illuminated, further increasing the voltage drop and causing the trailer lights to dim or go out.
Other possible causes include:
* A faulty wiring connection between the vehicle and the trailer
* A faulty trailer light socket or bulb
* A faulty trailer light relay
* A faulty trailer light switch
* A faulty trailer light ground wire
