My first step would be to check for a loose connection or a piece of burnt wire. If your batteries are at the correct voltage and yet your lights are flickering and the panel shows something less, then not all that voltage is getting inside to the fuse panel. With 13.5 volts at the batteries, it sounds like your converter/charger is working.
A corroded or loose connection between the batteries and the
12v fuse panel could be the culprit, as could a bad ground connection. Check them all.