Ok the RV type fridges. though in theory And I've seen absorption cooling units that were pure GAS no electricity at all other than the safeties and those... well they do not apply)
RV types use 12 volt to control operation and to ignite the propane. So if you do not have 12 volt (Battery power) in the trailer no joy.
Now how it works on gas.. When the Thermostat calls for COOL the control board opens the gas valve (A 12 volt device) and starts making 12DC into about a kilovolt AC (1000V) to generate sparks to ignite the gas.. After a period it looks to see if a thermocouple is generating a small voltage/current (IS HOT) and if so it keeps the gas flowing till the T-Stat says "I'm cold enough" .
Possible issues
No 12 volt
Propane off / out of (The instructions say turn it off when driving)
IF it works on propane when plugged with one exception the following do not apply
Spark gap too big (Very slight possibility it's "Just a tad" too big and the difference between battery and converter voltage is thus important. Very very low probability of this.
Spark gap way too big (Won't work on gas PERIOD)
Clogged gas jet
Bad gas valve
Bad thermocouple
Bad Control board
And the ever popular "Other issue".
One moving only.. IN some cases the design of the outer compartment causes the flame to blow out when moving. I've heard of it only never seen it in 12 years full time