Hey Bryce, thanks for reaching out. It sounds like the 7-round on your gooseneck trailer may not be wired correctly. Have you tried taking a wire tester or multimeter and checking all the wires? If the trailer plug is not pinned correctly to match the RV it would definitely explain the issue you are describing.
Or, if you are sure the 7-blade connector on your gooseneck trailer is wired correctly, you could use the adapter # PK12-724 to bring them together. The adapter really should not... view full answer...
LED lights do draw considerably less than incandescent bulbs so one easy solution would be load resistors like the # DI34ZR that you referenced since these simulate the amperage load of an incandescent bulb. view full answer...
The Super Titan Trailer Hitch # 38208 fits trailer frame width range of 34 to 34-1/2 inch so it would fit well on your 34-1/4 inch width measured outside to outside. view full answer...