Thank you William - your symptoms sounded perfect for the typical Master Switch problem.
So, it sounds like you have a wiring fault, which is fairly common in older trailers. Rats and mice like to chew on wiring and they can easily cause this to happen. And, over time, connections become corroded or disconnected, which leads to the same symptom.
We don't seem to have any owner's manuals for the 87 model year trailers, but here's a link to a 1990 model year one. https://www.hilotrailerforum.com/f49...-classic-2016/
HiLo published "generic" manuals for all their models in a year production, and, there was very little change in construction from year to year, so I suspect the wiring diagram in this manual matches yours. This one shows 4 fuses, and no Master Switch, so I suspect it is like yours.
I doubt your converter is bad. A faulty converter would not stop the interior lights from working directly from the battery. But, you are not getting DC 12V power to lights and probably a fan. My first guess is that you have a bad ground connection in the light circuits, and this could include the exterior lights too. It's going to take a tedious bit of tracing with a multimeter to find the problem, I'm afraid.