What would cause the brake light to remain illuminated on a 1992 Volkswagen Golf even when the car is not running?

On the left hand side by your steering wheel theres a swtich with a light on it. Press it. I cannot tell by your question WHICH brake light you're talking about. If it is on the instrument panel, then I don't know. However, if you're talking about the brake lights on the rear of the vehicle staying on, then the cause is probably a misadjusted brake light SWITCH. Or the switch could be defective.