What makes a 90 blazer back parking lights stay on?

It might be the brake lights. If it is, check the brake light switch connected to the brake pedal. It's right above the pedal and if it's slipped or adjusted wrong the light could stay on all the time. A brake light switch that is stuck like that can also prevent cruise control from working. On the other hand, if it's the WHITE light, it's probably the backup light switch that's stuck or adjusted bad. If it really is the parking lights, the fronts should be on as well.