I am not sure what brand/model power converter is in you 1988 camper. Or if it is still the original as a prior owner may have changed it.
If you post some picture of your power converter, fuses and AC wiring we can better help.
For some big picture things per your description, it sounds like you do not have a battery on your camper that is hooked up and still a good or good enough condition. The battery should power the lights inside with no shore power. Do you have a battery that is charged up installed?
Some of the older power converters needed to have a battery installed in order to work correctly. The newer ones, can run without a battery, but not necessarily all the older ones. Again, back to what brand/model power converter do you have.
Also, if you are not using a battery or a battery mounted on the camper, make sure the 2 heavy battery cables out on the trailer tongue are not accidently touching each other or the 12 volt DC + hot wire touching the frame. When the power converter is on, the positive 12 volt battery cable can have live power in it and touching the frame or DC negative can damage the power converter or blow fuses.
Hope this helps
Current Sunlines: 2004 T310SR, 2004 T1950, 2004 T2475, 2007 T2499, 2004 T317SR
Prior Sunlines: 2004 T2499 - Fern Blue
2005 Ford F350 Lariat, 6.8L V10 W/ 4.10 rear axle, CC, Short Bed, SRW. Reese HP trunnion bar hitch W/ HP DC
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