Since only the running lights were affected I would suspect the wire or connecter pin that feeds the running lights. This is usually the Brown wire, the contact nearest the ground connector which is the pin different than the other three. The problem could be the ground but I suspect that the turn and brake use the same ground as the running lights.
It could be in the MH or in the car. You may be able to isolate it by using a voltmeter or test light to monitor the voltage in various places while wiggling the wire and connector.
Edit:
OOPS! I thought you had a 4 pin flat connector.