A friend of mines kid has a 2006 VW rabbit that will leave the lights on when the keys turned off which kills the battery. They have been disconnecting the battery when the cars off.

They don't know if it's running lights that come on whenever the cars on or if it's the headlights stuck on.
There's no dinger going off in the car that the headlights have been left on. So I'd say it's probably the running lights.

I worked at an import salvage yard for awhile and I've worked on enough VW's to know I definitely don't want to dive into someone else's car blindly to fix something.

Anyone have any ideas on how I can trouble shoot and fix it? I think at this point they'd be okay with just disabling the running lights so they never came on but still being able to use the headlights/taillights at night. They talked to a VW shop in town and they wanted several hundred just to diagnose it and want to have the car for 2-3 days to do it.

I don't have the wiring diagram in front of me, but the headlights, or at least the relay if there is one, should be activated by the body module.

VAG may call it the comfort module or the Electronics module, but it's all the same part.  They fail constantly, especially in that era because the module itself is plastic with zero weather proofing so moisture kills them across all VAG models, especially the convertible Audi TTs

See if they turn off when p brake is engaged (supposed to)

I had the jetta for that year, and the head light switch is easy to pop out. you could unplug it instead of disconnecting the battery.
would also tell you if it is past the switch causing it instead.
I can't remember, but I think it was turning it past off that turned the body so you could pull it out of the dash.

If it’s the brake lights that are staying on, it is a small rubber spacer that the brake pedal rests against.

Over time that rubber spacer falls apart.

In a pinch you can use a plastic carpet tac from the trunk until you can buy a new one. I think I bought a dozen on Amazon for just a few dollars.

I had the same issue with a Gen 1 Tundra, yeah I know it's not a VW but hear me out. Pulled every fuse and relay I could get to in the lighting circuit but I still had to disconnect the battery to turn off the headlights, real PITA.

The problem was a fuse block that contained a control module for the alarm system, the module wasn't available as a stand alone part so the entire fuse block had to be replaced - thanks Toyota.

Thanks guys it actually was the body control module. I bought a used/tested one off eBay and it works great completely fixed the issue!

On my mom's 2012 VW, the fix was not this simple.  The brake light switch is screwed into the bottom of the brake master cylinder.  I had to remove the battery and air intake box and ducts under the hood to get to it.

Honda, toyota, ford, and chevy all seem to be putting the switch on the brake pedal as shown in the video.  VW been smoking the biden crack pipe when they put their switch under the hood.

Rad!