In some cars which have on-bord computer functions, an electronic module added with the towbar senses the insertion of the 13 pin plug and thereafter you get the same dashboard warning for the caravan as the rest of the car. Some get a bit too clever for their own good and leave you a message on the system too (e.g. my MB E220cdi). and you may get a false alram when starting up from cold the first time.
(I look on these things with a slightly jaundiced air. When I started caravanning in 1967 I made my own warning relay and light system using protected reed switches etc. and the details were published in the CC magazine En Route. I received many enquiries to buy, but failed to find a company to produce them at a sensible price and my day job didn't leave enough time for me to do so. I also played about with an early average speed meter for rallying but this too fell by the wayside).