Thanks everyone for your advice. We finally got it figured out!
We could not get the "auto" light to come on for nothing; the only indicator if our efforts were worth anything other than waiting it out to see if frig was going to cool:
1. Played with those two little buttons on the control panel like it was an arcade game--nothing--no light
2. then turned everything off and checked the GFI--reset them--no light
3. checked the breaker--reset it--nothing
4. looked at the frig fuse on the panel inside but did not pull it--it was good
5. pulled the outside panal off to make sure it was plugged in--tried again--nothing
6. then turned everything off (shore power) and tried to get the gas to kick in-nothing
7. finally, before going through the pain of moving the trailer around to ensure it being even (it wasn't far off center on the level's bubble) we pulled the fuse on panel inside and got a check light, only initially, then nothing--great!
--then with the "power" button in the "on" position the whole time pressed the "gas" button to the "on" position--the "auto" light came on and gas kicked in--re-connected to shore power--gas kicked off--"auto" light stayed on and been good since.
We guess the fuse wasn't making a good contact in it's slot because it's intact otherwise.
We are not very impressed with the electrical system in our Montana. We're very suspicious of our AC unit tripping its breaker as it has done this three times on two different trips. It makes us very nervous when we have the dogs in the trailer for a duration time-to-time while we are out and about....
Again, thanks to everyone who helped us out.