>>Has anyone found a way to test the fridge on gas
without putting it back in?

Yes.  Simply go to a supplier of propane or a good hardware store and you
can buy a flexible gas extension hose.  Screw it into the outlet where you
unattached the fridge and into the inlet on the fridge.  I'd probably do
this with the fridge sitting in the van, but if you buy a long enough
extension you could do it in your living room.  You could also attach it to
one of those portable gas canisters and have it anywhere.

>>3.) This is my real question: Attached to the gas
control unit (the little button you press and hold
while operating the piezo lighter on the pump knob) is
a single black wire.  This little black wire runs off
to under the sink where it just disappears into a
larger loom of wires and off into who knows where.

That black wire, if it is like mine, runs from the top of the fridge where
it connects to the thermocouple which allows the gas to flow into the
burner, or not if the flame goes out.  From there it runs where you traced
it and then to the back of the indicator panel where it activates the little
light that tells you whether the flame is going or not.

Good luck.

Paul