Ice maker.. You said it cycles so I'm going to skip just to the water parts and the possible problems:
During part of the cycle a cam shaft operates a switch,the switch is adjustable..(The adjustment screw moves the switch) so that the cam holds it open only for a precise period of time
This switch provides power to the water solenoid (Valve) outside allowing water to flow through the tube into the ice tray
Possible problems and suspect level Listed in CHRONOLOGICAL order
1: Switch adjusted to the point it never closes (very low less you've played with it)
2: Switch failed (low)
3: Broken wire (Low)
4: Failed solenoid (medium)
5: water line problems (varied)
5a: In-line shut off valve closed (low, unless you physically closed it)
5b: Frozen water line.. Supply side; Low unless you are in freezing weather
5c: Frozen line solenoid to ice tray (HIGH)
5d:Frozen water "Chute" inside freezer (HIGH)
5e: No water supply.. I assume you have water pressure elsewhere
There is also a low possibility of wire harness failure
Suggested test procedure
I like test lamps.. volt meters work too but are harder to read
Meter or lamp the solenoid electrical terminals.. Watch for solenoid power.. If none, suspect switch, adjustment, and wires
If power appears, then shuts off after a few seconds.. Did solenoid "CLICK" If yes, Disconnect water line from solenoid outlet and replace with any handy tube that fits over the fitting or another proper piece of tubing with a compression fitting (you can get ice maker tubing and compression fittings at most any hardware) again cycle.. do you get water out of this temp tube?
If yes, defrost freezer, make sure you can BLOW THROUGH the water line that goes INTO the ice maker
If you did not get water.. Make sure you can BLOW THROUGH the water line that goes INTO the ice maker.. and re-connect to solenoid.
now close shut off valve.. Oh, it was closed. problem solved.. No, it was open Disconnect water line from solenoid supply side, and re-route OUTSIDE, open valve SLOWLY, does water flow? no frozen line up-line. I'm not going to suggest a fix because that's not a ice maker issue.
If Ain't a Newell, It Ain't Wurt Oonin!