Info from DJ
Jeep Headlights stay on why
If you turn off the ignition before turning off the lights, they will stay on for 45 seconds as a "security measure," so you can get the door to your house open while it's still lit up or something stupid like that. Chrysler designed it this way this is what the Headlight Delay Module is for.
If you turn off the lights before the ignition, this won't happen or just cycle the key on and off again and the lights should go off.
I don’t think the HDM has anything to do with your headlights not turning on.
It is more likely that you have either blown a fuse or have a defective main headlight switch.
I hope you didn’t replace your regular headlights with those nice bright headlights that are on the market, because if you did that is your problem. Those lights use more power than Jeep & a lot of other cars on the road were designed to provide and require a complete headlight electrical upgrade.
Hope this information help. Post back if you need more help or what you do to solve the problem.