Great question!!
You have a good plan to supply the washdown pump from an existing through-hull fitting, typically either the galley
or head intake. A Y-connector lets the through-hull do double duty. Double clamp all hose connections below the waterline. Pumps push better than they pull, so
mount the pump as near the through-hull as practical. A check valve installed in the hose connected to the other side of the Y-connector will prevent prime problems and eliminates the need for manual valves. A second check valve is required on the outlet side of the pump to prevent backflow, but most deckwash pumps are equipped with this valve.
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You might find this article by Don Casey helpful:
Installing a Deckwash Pump | BoatUS
and these:
How to Install a Boat Washdown Pump | Boats.net Choosing and Installing a Washdown System | West Marine