I always keep my plug coated with die electric grease. It helps keep corrosion from getting in the plug. It could be a bad ground put a jumper cable from the truck frame to the trailer frame where you have no paint like a bolt head. If the lights come on you have a bad ground.
2010 Jayco Eagle Superlite 256 RKS
2008 Dodge Ram 3500 Cummins
66 nights in 2016
61 nights in 2015