With all other 12 volt systems working , when not on shore power , you have connection to the coach battery .
Here's where it gets confusing ; when you hook to shore power and the lights work ; that means somehow the interior lights are getting 12 volt power from your converter ( showing it's working ) and not from the battery .
Standard RV wiring would have all 12 volt systems , hooked to the battery; and the converter ( actually a converter/ charger ) also hooked to the battery to charge it, while on shore power . So no system powered directly from the converter only.
I'm as confused as you are , but I'll scratch my head for a while .
The other issue is that most times the RV interior lights would be two circuits so if one fuse blew , you'd still have some light to find your way around.
Are any of the 12 volt fuse you found labeled ?
JMHO: Unless a previous owner installed an inverter , I don't believe you have one ; but if you do the same would apply lights working inverter producing 12 volt power .