Probably the ice maker. Most refrigerator use the same manufacture of ice maker from China. If no success from above advice, then I would just replace the ice maker. Usually two screws, harness and bracket transfer, align the water tube, and that's it. Depending on where it's located about 15 minutes or so to replace it. If its in the bottom compartment it will be more challenging due to our older age.
My less than year old refrigerator ice maker started making popping sounds and quit working. The warranty repair guy said there were bunch of defective models made with cheap plastic gears that fail, plus they just fail after few years anyway. Not that hard to replace if you can find the model number you have, lots of places online to buy them.
You can Utube ice maker replacement see if it's something you can handle which will save service charge and labor?
If you don't want to fool with it, try Nichols appliance service co. 352-568-0300. he's does factory warranty work. Guy was very sharp and fast. I'm sure he probably makes several trips to the villages month? Good repairmen are hard find, I know it I need appliance worked on he will be my first try.