By discovering that the trailer's hazard lights work perfectly when hooked up to your truck, you have at least narrowed down the problem area to the motorhome and know the wiring on the trailer is good.
The first thing I recommend doing is taking a circuit tester like # PTW2979 and testing each of the pins on the RV's 7-Way while you have the corresponding light function activated. I have attached a 7-Way wiring diagram to assist. If the brake/turn or running light circuit isn't getting... view full answer...