My headlights stay on even when key removed but the turn signals still work

They problem showed up after accident. Correct? If so you have in all likely hood smashed wires in harness that runs along bottom of core support. Fixed many issues like this one from front end collisions on this model jeep. I would take back to repair shop and tell them its related to accident, which I can guarantee it is. Reverse lights staying on is the shifter detent cable was knocked out of adjustment. Put it in park, key off, go under car and find black plastic cable that goes to a lever on the trans. In the bracket that holds the cable pull back on the big half round clip, it has a slot in it for a screwdriver. After it is pulled back slide cable back and forth in housing make certain it moves freely. Than grab the lever that is on trans and push lever to rear of car. Push in clip and test that the shifter moves free inside the car. Than set park brake, key on, put in reverse, light should come on, push into park, light should go off.

Did you just buy this truck?

If you pull the 20amp park lamp fuse and the lights stay on, it almost has to be a short inside the headlight switch.
Will the lights go off if you unplug the headlight switch ?

Check battery after boosting car

I cant tell u the exact circuit but it sounds like u have an electrical short in the ignition system wiring harness.

Did you do some electrical work on the car?

I'm going to say you blew a major fuse or fuseable link wire you have not found yet.
The wipers need power from a battery source to stop, the headlights probably are on a battery circuit too. The turn signals would go thru the key switch but the hazard flashers would be also be direct battery.
You may need a wiring diagram (book) to find all of the fuses and circuits.

Check the battery and cables. Make sure your post clamps and any cables that connect to the clamps are secure.

Check the battery voltage. It should be close to 13 volts with the key off and doors closed, with the headlights on the voltage will drop to 12 or a little under. The headlights should stay bright for hours if you have a fully charged good battery.

If the battery voltage is low and the headlights pull it down even lower, the battery is ether bad or not charged. Try charging it if possible. If not take it to a auto parts store or battery store. They can charge it and load test it for you.

put your e- brake down when its pulled up even a little the lights go out to save the battery while the key is on during diagnostics

I took it to the Ford dealership. Don't ever let a shade tree mechanic work on your electrical. It turns out, someone wired the alarm totally wrong. Which shorted out my headlight switch.