Yep, easy peasy. I've done it myself a few times, though I'm not sure it's legal these days.
Easier if you have a wiring diagram, but if not, I simply take all the wires and wire them to the hitch plug. If the brake light is connected to an indicator, just swap em over. If an indicator is connected to a tail light, just swap em over, etc. until they ate correct.
There are no neutral or earth wires to worry about as everything is earthed to the bodywork.