Your "display" is just a sort of voltmeter. A full battery will be at about 12.7v and show as Full (briefly) then drop to Good, etc.
The converter makes 120v into 13.6v, way higher than a full battery, so your "display" will show Full. Note that means you can have a dead battery connected and with the converter on, the display will still show Full.
It also means that you cannot monitor on that "display" the rising voltage of a battery when being charged by the converter. It will show Full all the way up. It is when you turn off the charger and let the batteries sit on their own that you can tell how far up they are (after waiting a while for the surface charge to go away).
Note also that under load the voltage will be lower. So your "display" will show Fair with the furnace on and bounce back to Good when the furnace shuts off. After a while it will stay at Fair after the furnace shuts off. Means it is time to recharge the batteries!
1. 1991 Oakland 28DB Class C
on Ford E350-460-7.5 Gas EFI
Photo in Profile
2. 1991 Bighorn 9.5ft Truck Camper on 2003 Chev 2500HD 6.0 Gas
See Profile for Electronic set-ups for 1. and 2.