The wooden pump sucks water just fine, provided that it's either in water, or primed. It won't self prime more than about 3" or so. I could see the water climb about 3" through the clear plastic hose. No More.
I guess that while the clearance of the piston, and the valves was just fine for water, air just flows past them. I could do a better job, and add seals, and improve the valves, but now the engineering is starting to get to the stage where it's very time consuming, and fragile.
So, I'm just glad that I only made a mock-up, and did not spend a lot of time making it pretty.
Some you win.