Hello Markkram,
deep cycle battery is a very good choice. Not the problem. Converters back then weren't very elaborate, usually a large transformer inside, 1 maybe 2 selenium rectifiers, little else. Very basic, NO regulation!
Get a newer converter if possible.
There is also no isolation between batteries. If one battery is discharged, likely a fuse will blow as current from the fully charged battery will essentially be jumping it.
as far as testing;
Do any Rv lights work when the converter is powered by the AC input (with batteries unhooked or fuse pulled)?
does the fuse blow if all other fuses are removed? BTW, Holder should be cleaned and pinch together to get tight fit of fuse. a poor connection melts fuse element, a short blows gap in middle.
Easy tip; temporarily use a 12v bulb in place of the fuse that blows, (headlamp, fog, 1157, one which uses more than a "Test light" if current is flowing it will light up.
if it lights with all other fuses pulled and converter NOT powered on, the rectifier is shorted. replace complete converter.
If doesn't light up, re-install fuses 1 at a time to find which circuit is faulty.
also newer laws require a fuse or fusible link within 7" of positive battery connection.
thats to protect the wiring from battery on its way to the converter/inverter/chargers etc.
