Thanks for the reality check!
Looks like the very friendly free over-the-counter diagnosis given by the repair shop manager of the reputable RV dealer we consulted yesterday may not be quite right, so the issue may be more complicated than thought - not surprising with an old fridge.
We will continue to troubleshoot as best we can (any suggestions about how to do this most welcome) then if the problem persists consult with another technician.
Meanwhile, back at the ranchito, after we parked last night we restarted the fridge three times, the first two times it clicked through the start up sequence behaving just fine, then after staying silent apart from a couple of clicks for about a minute and a half switched itself to check.
We switched off the gas, removed the panel behind the fridge, checked the wiring etc and tried again. This time after about a minute we heard a noise like a bump, then we heard the gas jet starting and continue to burn (which we didn’t hear on the previous two attempts) and the fridge has ran perfectly since then?
Could it be there was air in the pipes that prevented the gas getting through properly, or a faulty electrical spark ignition mechanism that failed to light the burner on the first two attempts but worked the third time, or … ?