Don't confuse house wiring with DOT road wiring.
Dot wiring (the four plug) does not, and in my opinion should not, be grounded to the frame on a Scamp. Instead I always provide a ground back to the plug through the white wire.
Brown wire= Running lights
Green wire= Right turn/brake
yellow wire= Left turn/brake
White wire= Ground
Here is E-trailer's take with a lot of helpfull info.
Trailer Wiring Diagrams | etrailer.com
Note: They wire the ground to the frame, which I don't do since the trailer is fiberglass and the wiring can be inside the body with all connections protected.
Your "DOT" wiring is dependent and centered on your Tow Vehicle's wiring.
Your 12 Volt "House" wiring is dependent and centered on the house battery/converter.
You can add a harness to your TV to supply charge power to the House battery while towing, with the addition of a "two plug" or with the conversion to an RV plug.