TeJay I will take your advice and get a load test.
I sent an email to Winnebago about this issue. Check out this great response:
"Subject: FW: 10R76447, battery questions
You will want to disconnect the cables when you are going to be externally charging your batteries.* The battery mode solenoid is what controls the battery boost switch, inside your chassis electrical box is the battery mode solenoid and coach battery disconnect relay. This box is located on the driver’s side of the motorhome inside an exterior compartment just adjacent to where the batteries would be on the other side in the step well.* When the ignition is on the solenoid completes the circuit and the engine’s alternator charges the house batteries, when ignition is off it would break the circuit thru this solenoid. Likely the clicking you heard was from this chassis electrical box and the solenoid or relay.* The battery boost may have been stuck at the solenoid which wasn’t allowing you to use the battery boost option. It is possible that your chassis battery was way too low as well.
Also here is another email I sent back with a theory about how the battery was killed:
Sent: 2014-04-25 13:26:31 GMT
Subject: Re: 10R76447, battery questions
Thanks for the comprehensive response. I believe you are correct that the battery voltage was very low resulting in the relay or solenoid cycling.
Also I have a theory about how the battery was drained that needs to be verified. There are reading lights installed on the wall behind the driver and passenger seats. The power for the light on the passenger side is supplied by the coach batteries. The power for the light on the driver side is supplied by the chassis battery via the dashboard lights illumination intensity switch. This roller switch must be rolled all the way up to supply power to the light. It sounds like a relay is energized when the switch is in this position. Since the map light was turned off using its integrated switch, yet the roller switch was still in the up position, could this have been continuously supplying power to a relay and draining the chassis battery? By the way the wiring diagrams I found on the Winnebago site do not seem to show the light wired via the roller switch."