If plugged into shore power, does it matter if the battery switches in the battery compartments are turned off or on?
In my GT 378 if the batteries are disconnected (storage mode) they are not being charged while on shore power. I have a rocker switch (momentary up and down with center detent) that is illuminated when shore power is applied but it is not an indication that the batteries are tied to the bus. I must actuate the switch to the momentary connected side (up) to insure the battery is connected. It doesn't matter if the switch is off or on when on shore power (converter will provide 12 volts to the coach) but the batteries will not charge if not selected to on. This is how my unit functions. P.S. Genset same as shore power.
If you have a 12 VDC receptacle in your trailer , go and get you a plug-in 12 VDC monitor and plug it in. I keep my plugged in all the time. It usually reads 13.6 to 13.2 VDC. I usually keep my trailer plugged in shore power even in storage. Also, out camping without plug-in power, it will show when you need to recharge the batteries.
I had an extra half hour yesterday, so I measured the voltage across the chassis batteries whilst attached to shore power. I did have a couple of radios plugged in a playing in the coach, so I'm not sure if the inverter/charger was at that moment giving priority to the house batteries.
I got a reading of 12.85v and feel good about that since it was sitting for two weeks with some temps of zero reached. I'm pretty confident they get a charge when the house batteries are topped off.