My F-500, I had both commercial and RV plugs plus flat 4 and round 5. All would work the lights and brakes on most trailers. (often would plug semi trailer in to test lights)
Ever wonder why the hands that got to run, got to have lights don't mess with the RV style? If there is corrosion in the contacts because the trailer has not been used? Few seconds with a small round wire brush, good to go. Now try to clean the slots on RV style. The plug loose in socket? Use a screw driver in the slot in pins, spread just a little. Now it fits tight.
Another possible benefit of putting a commercial on the RV trailer; Mr Stealit might think about the rare LEO that would check out the trailer that doesn't have lights...