First off, am I correct that you have a flat 4 connector on the Edge and a 7 pin round POL connector on the trailer with an adapter between the two? Why does the camper have a 7 pin connector? What functions might you be missing with the flat 4 connector only supplying running and brake lights. For starters, the battery charge circuit for the camper isn't working. Can you get someone to install a 7 pin round connector on the Edge and eliminate the adapter?
If you got the lights to come on by any method why are you asking for help? Did the lights fail again? Did you try the battery trick again? What were the results?
Bottom line is that someone is going to have to make sure that all of the lines in the camper are getting both power supplied and a good ground connection to the Edge.
You are going to have to get a voltmeter and check voltage