Why would the tail lights stay on even when the car is turned off on your 1992 Honda Accord?

it would most likely be a bad or maladjusted stop light switch located on the brake pedal assembly

There is rubber plug that is attached to the arm of the brake pedal and presses against the brake light switch. When the brake pedal is depressed the plug no longer presses against the switch. this causes the brake lights to come on. If this rubber plug is broken or missing the brake lights will stay on all the time.

I fixed mine by duct taping a piece of plastic over the hole in the brake pedal arm where the plug goes.

The website listed below, under Related Links, is a blog post describing how to do it. Or you could go to a Honda parts dept and buy the correct part for a measly $2.