If no clicking that means you starter has had it, easy to fix, most times you can replace it yourself.

The Piezo on Thetford fridges gets sooted up. Before each trip away I have to clean it so the fridge will light. You have to remove the bottom airvent on the outside of the van to access the rear of the fridge. There is a small wind shield around the burner you need to remove, one screw, and the Piezo igniter arm sits just above the burner. Often you can knock the soot off it by giving the igniter arm a couple of light flicks with a piece of stiff wire, but sometimes I have had to get in their with a small needle file and give it a bit of a brush up to clean the surface. Mine is the non electrical type of Piezo that you have to keep pushing the button but it would apply equally to the electric type. You might need a new one but try desooting first, as no spark no click. It is the spark jumping across the gap that causes the clicking sound.