I had to repair my ice maker for the same symptoms. Either no-fill or
inadequate fill. The problem was the timer motor contacts for the
solenoid were burnt and corroded. Crappy design reminiscent of
failure prone washer machine timers.

Anyway, the problem was very obvious as soon as the face of the
icemaker was removed. I cleaned up the contacts and used some epoxy
to fill in where the surrounding plastic melted. Been working for 4
years since that repair.

One other warning: Unplug the fridge before you remove or work on the
icemaker. There is 120 volts on the internals and the connector
(which may or may not be adequetly protected against prying hands).

-Chris