Started by replacing icemaker module - worked for a while
but water supply tube was iceing over and eventually stopped making ice again.
Next step was replacing solenoid - 1/4" copper pipe connection to new solenoid leaked so trip to plumbing store (got a new ferrule to remake connection).
The white translucent tube the runs on the back of the fridge between solenoid and icemaker looked black on the inside - replaced (another trip to the store). Seems to be making ice now.
I think I'm going to put a water filter inline (currently there isn't one and whatever that black stuff is, we're drinking it!)