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The problem is that the plastic pump plunger/piston sticks in the cylinder. Use 120 grit sandpaper and EVENLY sand the circumference of the plunger head and the 2 ribs below it. Test. Repeat until there is better movement but NO loss of suction.
Photo 2 shows the plunger/piston sanded so it works nicely in the cylinder without having taken off too much material - you do not want to take off too much. It doesn't need to be super pretty smooth but sanding too rough and uneven will not keep suction. Sand a little at a time and test it at each and every attempt.
When you are satisfied put a small amount of petrolium jelly (Vaseline) around the plunger/pistons head and ribs.