Each engine should have it's own battery.
Genny could have it's own or share one of the mains.
Since the 3000 doesn't have a 'house' bank, wiring is a little wonky using the two "1-both-2-off' switches. The placards make it even more misleading.
Stick your head up under the portside gunnel from the ER and look at the switches. Tracing the incoming battery wires will help illustrate what is switched and what isn't.
Additional Info....
Once I traced what the factory did, I did change my setup.
To have the "proper" setup one really needs an additional switch, hence Maxum didn't go that route to keep to a cost point on these models.
Standard practice with the 1-2-Both-Off switches is to have the Load on the common terminal and the source/supply to the 1 or 2 terminal. This way you can select the battery desired for operating that load. (Both is handled internally to connect them in parallel).
To serve the house with the same flexibility, there needed to be a 3rd switch to allow for selecting which bank was serving that load.