Your description is not clear but I think you are asking how to get the trailer's park/running lights to work, correct?
If so, first check the #5 fuse in the underhood Distribution Box. If that's OK, it could be the Park Lamp/Trailer Tow Relay, also in the Distribution Box. You can do a quick test on this by swapping with another identical relay in the box. Beyond those, you're probably talking about a problem with the brown/white wire or its connectors.