If you want to fully test the refrigerator, then you will want to put it on a nice level surface, plug it in, put it in "electrical" mode, set the thermostat to max, and then come back the next day. If it is cold, then this suggests that the electrical heating element is working, the thermostat is functional, and the coolant gas system is intact. Now, turn it off and wait for a day for it to warm up again.
Now connect a 20 lb cylinder to the gas fitting. I have a propane fired burner assembly that I disconnected the propane line from, and amazingly, I was able to make that up directly to a fridge I was bench testing. Put the fridge in "propane" mode, and light the pilot light and wait another 24 hrs to see if it cools down.
I don't think your fridge requires a 12V
supply, as the propane is ignited with a piezo ignitor, rather than a battery driven auto-reignitor, and it is not a 3-way fridge.
If the fridge has truly never been run on propane, then chances are if it works on 120V, then it will work on propane as well, since they are using the same coolant system for the cooling. The thing that usually wears out/goes wrong with the propane system is the the "chimney" gets rust and rust flakes fall down on the burner assembly and mess with the flame. If it has never been fired that way, then it is probably fine.
Now the warning--I have the user's manual for that model of fridge, and it was published in 1996, so that fridge is potentially aging. Check the rubber seals around the doors to make sure they aren't getting hard/brittle, and check all of the plastic pieces to make sure they aren't cracking with age.
On the other hand, I paid $300 for a used fridge of the same vintage with a broken hinge on the freezer door. If I had known thenwhat I know now, I think I would have negotiated the price a bit more actively.