Running lights on my Mini-Lite have dual conductors. They are not grounded to the frame. If you find the same to be true on your RPod, consider whether the ground problem (if it is a ground problem) could be on the truck end of the trailer connector.
There's probably a junction box screwed to the frame under front of the trailer. It's where your trailer umbilical cord connects to the running lights and trailer 12V power. Check there to make sure all connections are good. Also, check both the plug and socket for the Bargman 7-pin connector.
- 2016 Ford F-150 SCrew Lariat 4x2 3.5L Ecoboost, 1700# payload
- 2020 Rockwood 2507S