FYI, thanks to Linda Cain, ACA webmistress, for posting
Dometic's 1999 8-page Troubleshooting Manual for AC/Furnace
and a later and very comprehensive 134 page AC-Furnace Troubleshooting Guide
centering around the "Comfort Control Center" commonly referred to as the thermostat.
Both these documents appear to have been superseded by Dometic by a 2 page thermostat brochure (I asked & that's what came up & it isn't very useful). These are way more detailed (and in fact cover a whole lot of stuff Alpiner's won't care about like basement AC units...) and should provide for hilarious night time reading for the whole family to enjoy.
As to furnace control & AGS, their tech folks state emphatically the only thing the Dometic thermostat does is turn the furnace on/off as called for from the temp, and the generator on/off if called for to run AC or heat pump action by a roof unit. Well OK then. Happy diagnosticationalizing!!