This isn't my exact area of expertise, but I think on that 4 stroke motor the valve is open in the normal position, when the engine is cold, and as the temp comes up it closes to bring the mixture back to normal. It does not pop in and out like the old choke solenoids did. I would recommend the factory service manual as a reference for servicing the system. I think you are on the right track, but may not be looking at the system exactly as it works. The voltage that controls the enrichener is like 5 or 7 v.
Try boatinfo.no to access a digital copy of your manual. It is a tricky site to navigate and not always up, but they have a copy of every Merc manual there for all to see. I have a digital copy of that manual here too, but I cant look at it now. I'll check back later today, or you can PM me. I don't work on them a lot, but do have one good customer with one, so I see it every year.
One thing I did see on those motors that caused a similar issue. When you drain the engine oil from the drainplug and then put back the 1.6 litres it calls for, the engine will be over filled with crankcase oil. It does not all drain through the plug. When it is too full it starts hard and doesn't want to idle
2006 Forester 19 Fish (new deck and carpet, Pontoonstuff interior, 2019)
1996 Mercury 50 ELPT4S
1983 Sea Nymph FM171 Striper (complete rebuild from hull up, 2014)
1985 Johnson 70 J70ELCO
Raystown Country, PA