I would start by putting a meter on the RV plug to see if there is power there. That would determine if the problem is with the Jeep or the RV.
Do you have a friend with a pickup or some other "tow" vehicle? You could hook up the lights of the jeep to another vehicle to see if the lights worked on the jeep. Again, this would tell you if the problem is with the Jeep or the RV. You could also hook up a utility trailer or dolly or something to the rv to see if it lights up.
I don't see anything on that fuse panel that would affect your vehicle lights. For what it's worth, most electrical gremlins I've had over the years on trailer lights were from bad grounds.
If you can test a couple of these things above then post back someone can help.