You obviously have the requisite 12V if the fridge operates at all. What you may not have is an air-free propane supply. With the fridge on the Auto setting, the fridge will detect if 120V is present but if not, it should attempt to light but... The fridge will make three attempts (clicks three times) to light and will be locked out (check light comes on) if lighting failed .
Why would it fail?? Most commonly, it is too much air in the gas supply which will occur if the supply was just turned on and the propane has yet to be used. Lighting the stove and letting it burn sometimes helps as the stove is not as fussy about air in the line. Sometimes when trying to start the gas operation it can take 5-6 tries by resetting the fridge (by turning off and then on) after each failure. However, if you expect an automatic flip-over and light up the first attempt without having purged any air in the propane line, you are asking a lot. Once the air has been purged it should generally light quickly enough. (To force lighting on gas without it testing for 120V first, simply leave the 'Auto' switch off.)
Another common problem with failure to light is spider webs in the burner area. Spiders love propane but their webs can disrupt the propane flow to the burner dispersing it enough to cause a failure to light. Carefully cleaning out the area is the solution.
A problem with the PCB would be a last resort type of problem, but not impossible, IMHO.