One thing I suggest.. is to use a test light. Find the converter (if it is not the inverter) and disconnect the negative lead from the battery Now at the converter Clip to minus (Black) termial tip to red.. BRIGHT... good.. No light. Found your problem.
Move down the power line to the fuse block, the fuse or breaker or switch between fuse block and battery..
Problem exists between bright and dark.
NOTE With fully charged batteries if you have BRIGHT at converter without being plugged in.. you know it's the converter.