RE: Aux Battery Mystery
Tim, what lights are you talking about when you say the lights don't come
on?  I talking about the headlights they do turn off when the ignition is
off.  The side marker/turn signals stay on though and will still run your
battery down over time.
The interior lights should work all the time.  That includes the light over
the storage behind the stove.  In many cases when an aux battery is
installed the interior lights, radio and cigar lighter wiring is changed to
be on the aux battery.
A properly installed and working aux battery is connected to the starting
battery and being charged when the engine is running.  When the engine is
off the aux battery is disconnected from the charging circuit and starting
battery.
The refrigerator should work when set to AC and there is shore power
plugged into the van.  It will cool slowly so give it some time.  It should
only work on 12v when the engine is running.  12v shouldn't be avialable to
the refrigerator when the engine is off.  It will kill an aux battery in
about 2 hours.
As you suggested put a meter on the aux battery and see if it has a
charge.  Then check it with the engine running and you should see about 14v
at the aux battery if the charging circuit is working,