Propane Fridge problem

I would start by cleaning- if the burner and/or orifice is dirty, when it goes to low flame, the flame will be too small. IIRC, the 46E was the new style cooling unit and burner, so I would soak the orifice in alcohol and air dry, clean the burner. Another issue with some of those old models is there is an LP filter in the line. After all these years, the filter gets clogged. I think it is removable on most models, but not sure.
The ignitor should be the piezo type, and it should snap when pushed, producing a spark. If it does snap but doesn't work, it's probably shorted somewhere.

I have a couple of service manuals that should help- the non electronic model diagnostic manual, and the older RM manual- the older one has the RM46, just not the E, so much is different.

1984. I think those had a pilot not an electrical ignighter. The pilot heats a safety probe which keeps everything running. If that is your system you need to replace that unit. Think about $30. It probably is right at the end of the pilot line tube. Either a small tube or couple of wires go to the main gas valve from the pilot assembly. In the old days we had to light all the pilots for fridge, furnace, hot water heater etc.

There is your problem

I have never used a propane fridge before so I am trying to learn all the knobs and buttons but I'm pretty sure the igniter does not work.

Is the igniter working?