If your vehicle is showing brake lights stay on even when the car is turned off, here are the most likely causes and the parts you'll need to fix each one.
Many vehicles use a small plastic or rubber pad on the brake pedal arm to press against the brake light switch. Over time, this pad becomes brittle and shatters, leaving a hole that prevents the switch from being pressed when the pedal is released.
The switch mounted above the brake pedal can fail internally, causing the electrical contacts to fuse together. It can also vibrate loose over time and back away from the pedal arm, making the car think the pedal is always being pressed.
Forcing a single-filament bulb into a dual-filament socket, or jamming the correct bulb in backwards, can bridge the parking light circuit to the brake light circuit. This feeds constant power to the brake lights.
In modern vehicles, the brake light switch doesn't power the lights directly; it sends a signal to the BCM, which then turns the lights on. An internal short or software glitch in the BCM can cause it to supply constant power to the brake lights.