When I got my trailer, the running lights didn't work. I replaced them all with new LED fixtures, cleaned the rear tail light fixture sockets with a wire brush in my Dremel, and replaced all the bulbs . . . even the ones that worked or "looked" fine. When I tested, they all worked. The common ground on my trailer was located at the 7-way connection area. I soldered all the grounds together and bolted the lead to the body with a new wire and a new bolt.
My "kit" consisted of a small battery charger, a 7-way tester, a small multi-meter, a 12 volt
jumper light, soldering gun, map torch, and an OEM wiring diagram.
The previous owner had disconnected the breakaway switch. I installed a new one and reinstalled the towing light fuse panel that had also been removed. I rewired the 7-way connection using the 7-way tester and installed a new umbilical cord. I ignored wire colors and wired everything (by function) to the standard 7-way tow vehicle connector using the 7-way tester.