Rick,
The primary valve is as you describe - single input and output. It is possible that the valves are connected incorrectly. Did some more experimentation. The water dispenser "path" works, while the ice maker path does not. So I switched water valve connectors. The yellow wire connectors are now connected to the brown solenoids. And the conditions changed.
Now, when the water dispenser is activated water is released by both the dispenser and the ice maker. It does make it easier to reproduce the issue as it is now not necessary to wait for the ice maker harvest cycle. I did not mention that when the problem occurs there is a very noticeable buzzing sound, like a relay that cannot completely engage.
I had thought that the sound was originating at the water valves, but since switching the connectors and being able to reproduce the issue a will I am not so sure of the origin of the sound. It sounds a though it might be coming from inside of the refrigerator. What is the source of the logic that controls the opening of the water valves?
Already replaced the main control PCB because of a post found on a different forum but that did not help.