Why Do My Truck Brake Lights Stay On. Several things can make this happen. Something as simple as the Brake Light Switch sticking will make your Brake Lights stay on. Another reason the Brake Lights may stay lit while driving is a shorted/melted fuse panel. Bare wires in the wire harness for the brake lights can be hard to find. Sometimes the best fix is to replace the whole wiring harness. If your Truck has Brake Lights that stay on or don’t work at all give us a call we can fix any of your electrical issues that your Truck may have.