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No 'clicking' sound-make sure 12v is present at the fridge. Check any fuses and make sure your battery is fully charged and supplying power to the TT. When you unplug from shore power the trailer battery powers the circuitry that runs the auto ignition cycle for the fridge.
If your trailer has been stored for a length of time, the gas lines will bleed out. Light the stove first to get the air out of the lines and then it will get to the fridge quicker.
My fridge still takes about 3 attempts to light after bringing it out of storage and bleeding the air from the lines by lighting the stove.
2006 23B Hybrid with 10k round bar WDH
2011 F150 4x4 SCREW Ecoboost, Max Tow, Integrated TBC, 3.73 LS axle, Firestone Ride Rite airbags.