Generally those ice makers are U-LINE but what I'm about to say applies to all of them (U-Lines make Ice Cresents. like a half moon)
First to cycle they have to get down to around 25 degrees. I gather yours is getting there so skip this paragraph.
As it cycles a motor starts. a cam or two start to rotate the shaft is the "Fingers" (ice pusher) shaft. on another model it is the ice tray itself and that's about the only difference (That one makes cubes)
A switch closes bypassing the thermostat and a heater starts. as the ice pusher fngers encounter the ice the motor stalls. soon as the surface of the ice melts the cycle continues. The ice is pushed out and anoter switch closes. this switch is adjustable (The +/- adjustment screw under the front cover) and it sends power to the solenoid. water now flows assuming the manual valve is open.
Suspects are the Switch and the solenoid and the tube from the solenoid to the ice maker in reverse order of likelyhood.
To test the switch take a knife (Table knife) which a magnet will stick to.
Have partner force cycle Ice maker while holding flat side of kinfe about 1/8 to 1/4 inch from side of solenoid magnet Should be attracted during cycle
Also observe of water going everywhich way but into the ice tray.
IF no water sprayng about and magnet attracts knife
Remove solenoid outlet tube (To ice maker) and try to blow through it. Should be like blowing through a straw. if hard to blow through tube is obstructed. Please do not ask how to clean.
Also look for water dripping from above. IF YOU SEE water anywhere (Before removing tube) bad.
now connect a short tube to solenoid outlet and re-cycle ice maker. NO water at this point = replace solenoid.
Now their are about 100 different solenoids.. costing from about 10 bucks to around 100 dollars. They all work exactly the same and either have the same connections or adapters. the mounting brackets may be different. So don't speing more than 25 bucks.