You need to clarify whether or not you want to use the car's electrics to charge a leisure battery and/or other supplementary stuff on the thing being towed.
As far as just ordinary towing is concerned. A 13 pin connector is only the same as a 7 pin except it gives you reversing lights and is standard on modern towables.
My car trailer has them and I had an adaptor fitted to it so that I could plug it into my old 7 pin socket. It works fine.
Here is a wiring diag thatg shows you what to connect up if you want ignition live or permanent live, or both as well as the rest of the stuff.
Connecting the electrics is a vital step in fitting a towbar. With our 13-pin wiring diagram and table we make your job quick and easy!
www.ecs-electronicsuk.co.uk
If you want ignition live it may well be best to connect it direct to the battery but via a relay driven by the ignition live.