After turning off the propane, disconnect the propane lines then pull the fridge about 10" inside the camper. Should be able to disconnect the thermocouple on the safety valve at the top. Gently clean to remove tarnish buildup. You can use an eraser or 600 grit paper. Then, best you can try to clean the valve side, again gently. I have used a very small piece of 600 grit on the end of a finish nail head to gently rub back and forth then blow out. Clean good and reinstall.
The wire kit replaces a couple of wires at the top of the fridge with extra low resistance wires. This was actually a recall a few years back. Thought I was having the problem at one time, but just made my own jumpers. You just need to make sure you have extra good contact as even 1 ohm could stop it from working. Wouldn't wste the money on a $20 kit.
