As Frank mentioned, most likely a bare spot somewhere. I had the same issue, if sitting still the lights worked for hours, no problem. Hit the road and 10 minutes in the running lights fuse in my '11 Chevy full size. My wiring was old. Obviously, the issue was a bare spot that would make contact as the wires bounced around while underway.

If your wiring is old, like mine was, you may find the problem is not confined to one spot, and it is simpler and less time consuming to buy the waterproof led full light kit at harbor fright or wallymart or your local trailer shop, etc.

Just my opinion, I chased it a few days and to be honest, the led upgrade was worth the investment. Good Luck!