What would cause the rear parking brake lights to stay on and drain battery of 1992 Lumina when car is turned off?

The brake lights will stay on if the switch is either out of adjustment or damaged. Pull up on the brake pedal to see if it will go out, if it does, you might be able to get by just adjusting the position of the brake light switch. BTW, it's on the brake pedal mechanism, under the dashboard.