ALL RV refers the freezer gets COLD before anything else, that is normal on your refer.
Check light is a code ONLY for LP failure to light or stay lit. There is NO indicator when the refer fails on 120 volts, it just will not cool
There is NO pilot, it is a regular flame
Need Model number, but I will bet it is impossible to read after all these years.
When was the last time you cleaned the burner and the Chimney for the burner flame? IF NEVER, then that is where you have to start as the burner area and burner probably has debris and rust.
If it fails on both 120 and LP and you verify you have NO RV 12 volt supply problems, then your main circuit board is probably bad. Doug