2000 Dodge Intrepid Backup lights

When you shift the car into reverse the transmission has a switch on it, this signals the transmission control module and body control module which sends a signal to the front relay in the engine power center(another module is there) where these relays are placed along with all the cars fuses. The relay may have a problem and is stuck closed. If the switch was bad it shouldn't make them operate with the key off. If I hear of any bulletins about a software error, I'll get back to you. For now, try swapping relays with another with the same part neumber and see if this helps.
It may or may not be serviceable seperately from the front module. A new feature that started in 2000.