There are several reasons to explain why your brake lights are continually staying on and won't shut off. For the most part, this could be due to a malfunctioning brake light switch. If the brake light switch won't cut the signal that's lighting up the brake lights in the first place, naturally, this will allow the brake lights to continually stay lit indefinitely. Otherwise, the brake lights might be lit up because of simple driver errors, such as unintentionally applying pressure on the brake pedals. If not, you could consider checking the CAN Bus System, which is how those aforementioned brake light switch signals send input from place to place.