Nobody has mentioned this so I will. It might help understand the strange things that happen when the ground is poor.
Current flows from Neg to Pos, not Pos to Neg. Electricity is the flow of negatively charged electrons which are stored in the Neg half of the battery. When a circuit is closed, they flow out through the ground wire, through the appliance, and back to the Pos post on the battery.
The ground on a vehicle is usually a battery cable bolted to the frame somewhere near the battery. All appliances are then bolted to the frame, too, either directly or indirectly. This is why, when attaching any electrical device to a vehicle, they tell you to disconnect the NEG battery cable, to neutralize the car body which is essentially hot all the time. Early cars had a positive ground system. Most of them switched in the '50's. I don't understand the chemistry here but they were having problems with the copper wire corroding with positive ground.
For the current to reach trailer lights, it has to flow through the entire car frame to the light plug, then through the trailer. There are miriad ways for the current to get blocked. That's why it's safer to run a special ground wire all the way from front to back, or at least through the trailer if your light plug on the car is grounded to the frame. It's to reduce the resistance from all the connections.
If there's a ground problem in the car, it can cause problems with all the appliances, not just the trailer lights. If a reduced current is all that can get through a dirty ground connection on the car, it will cause the current to be reduced on everything. If an appliance in the car isn't getting the full amps it needs to run because the trailer connection is syphoning off the juice, it can do some strange things in both the car and the trailer.
If the bad connection is on the pos side, it will only affect that particular appliance.
I'm just theorizing here because I don't really know. Note that many cars have the neg battery cable bolted to the engine, not the frame. That might degrade the connection when the trailer plug ground is connected to the frame. In that case, it might be better to run a special ground wire for the trailer all the way to the battery.
