I found this out quite by accident, but it is described well in the manual (which I didn't read until now). The battery switch next to the door has two positions, "store" and "use" (or something to that effect). When in the "use" position, the light is on. It is also on when when plugged into 110volts regardless of the switch position. I assumed that when it was on shore power the charger was always connected to the batteries. Not true, at least with out 2006 Bambi 19'. If one is plugged into 110 volts and the battery switch is set to the "store" position, the batteries are not connected to the charger. This is great since one can avoid overcharging one's batteries.
It would be nice if the switch had more than one light to show this condition (i.e., charger connected to batteries or not connected to batteries) but it doesn't. So I installed a plugin volt meter which shows the battery voltage. See the attached photo. These are available from numerous sources on eBay and elsewhere. When the charger is connected, the voltage will show over 13 volts, and when disconnected around 12.7 volts (depends on state of charge). When turning the switch to "store" while plugged in to 110volts, the battery voltage will not instantly return to 12.7 volts, but will slowly drop as the battery assumes its normal voltage without the charger applied (see pics). Note that the wall 12volt plug always shows the the charger voltage if plugged in. It is not affected by the battery switch.
So there does not seem to be a need to add a separate switch to isolate the batteries from the charger.....just hit "store" while it is plugged into 110v and the batteries are isolated from the charger.
And there does not seem to be a problem in running the charger without the batteries attached.... that is the way it is setup. With the batteries disconnected the lights and other 12 volt
systems are run by the battery charger.
Further there does not seem to be any reason to have an A/B switch. Such a switch makes sense if you are reserving one battery to start an engine (as in a boat or motorhome), but I don't see any reason to use on in an Airstream.