A few months ago I noted that my new Maytag French Door bottom freezer refrigerator made clicking noises sometimes when it was running. It was intermittent and I had not called for service because I figured I needed to tape record it so I could play it for the repair guy. Besides I have an extra 4 years service agreement on it from Lowes at a cost of $99.
In any case the appliance repair guys here suggested that it was a bad overload protector or something similar. It did not sound electrical to me. Somehow I felt it had something to do with the water in the door. It has 2 tanks in the back of the refrigerator (inside to keep water cool) and I wiggled them a bunch and also I wiggled the hose where it goes into the inside back wall of the refrigerator in case it was touching something internal where it was routed. There was definitely an inch of play there.
Well that seems to have solved the problem. I don't know if there was air in the line or the line was making noise like a hammering or expanding water pipe but it seems to be pretty much gone.