What you have suggested are essentially the things I have done previously. This is not a problem where things quit, but where the quit and them resume working. However, I am going to try what you suggest again.
When I began earlier, the ice maker was not making ice, and was dry (no ice cubes or water in the ice maker. There was no water coming from the water dispenser in the door. I had unplugged the refrigerator before emailing, and had taken the ice maker off of the hanger hooks, so I rehung the ice maker. The fill tube was not blocked with ice.
I plugged the refrigerator back in and ran a jumper between T and H. The ice maker cycled correctly, and water went into the ice maker from the water line (it was dry when I took it off the hangers). I checked the water dispenser on the door, and it has started working again.
So the ice maker now appears to work correctly for the moment, and so does the water line. Nothing seems to have been frozen up, just not filling and/or cycling. This is the recurring problem I have--sometimes they work, sometimes not.
I need a better answer that explains why it sometimes will not make ice but still dispense water, then other times neither will work. It isn't a water line problem. Frozen lines would not unfreeze to allow water through intermittently, and if the ice maker stopped cycling, why begin again? This seems to me more of a electrical problem than a mechanical one. Unplugging the refrigerator and then plugging it in might have more to do with making it work than the mechanical parts. Do you think that could be the answer, and if so, what would stop/reset if the power is unplugged? I'm not questioning your experience, but looking at the situation here and how the tings I have already done, and the things you suggest, do not appear to fix the problem.
OK, so I placed a thermometer in the freezer compartment. It dropped to 0 degrees F. So now it is cycling, and the temp is below 10 degrees, so those reasons for the ice maker not working can can be dismissed.
That takes me back to my original post. None of your suggestions to this point solve my problem--they merely confirm that the ice maker appears to be OK.
What else can cause intermittent stopping/starting of the ice making process and the water dispenser? Does the ice maker control the working of the water dispenser? You have not said, and that would seem relevant to solving the problem.
OK, I will order another ice maker and see of that fixes the problem. It will take several days to get one. After installation I will send another reply to let you know how it is going. If there is still a problem, we will go from there. That will be after I submit a rating, but you said that was acceptable. Thanks for your help and patience.