I'd like to thank all members for their replies. As mentioned, I hoped the info I posted would help others but as it turns out it helped me.
Winnie tech line confirmed that a relay is supposed to connect the coach batteries to the chassis battery circuit (and thereby to the alternator) when the engine is running. He said it is not voltage-dependent (i.e. the coach batteries do not have to discharge to a certain point before this happens).
So it sounds like mine is mis-wired or otherwise not working.
I also learned that some wiring diagrams are available. Go to WGO.net (http://winnebagoind.com/) then click on > Resources.
And he confirmed that neither the generator nor shore power charge my chassis battery.
For now, I'll just use the switch I installed connecting the coach and chassis batteries if ever needed -- the relays are very difficult to access.
