I have a 2011 7P Touareg with incandescent tail light bulbs. My trailers all have LED lights. What I find is that everything works as far as the trailer lights are concerned, but the car computer shows a "check trailer tail light" error when the trailer is connected. It thinks the bulb is blown as not seeing enough current.

The car has the VW tow module installed - so it is integrated into the whole vehicle management system. The trailer lights are wired into the module, not the car tail lights.