First thing is to have a volt meter and a 12v test light. The 12v lighting in RV's usually spliced off a main wire with cheap connectors and from the sound of things your dealing with a bad connection.
Are the lights switched at the ceiling or powered from a wall switch or both ?
What brand and model is the fridge?
We'll see if we can find a troubleshooting guide.
99DSDP 3884, Freightliner, XC, CAT 3126B, 300 HP /ALLISON 3060
2000 Caravan toad, Remco & Blue Ox.