The most common cause of brake lights that remain on when the car is turned off is an adjustment problem with the electrical switch. Depressing the brakes activates the simple electrical switch that is located near the brake pedal arm and turns on the lights.
There are some additional possible causes of the brake lights staying on. A hydraulic switch is located near the master cylinder under the hood, and corrosion or other minor damage may keep the switch stuck at an "on" position. In this case, adjustment is typically not possible, and the switch must be replaced.Another possible cause is an issue with the vehicle's electrical system overall. In this case, the complex system typically will require professional repair.