The central rod and “T” handle are made from 3/4″ PVC pipe, which can be sealed to keep it from filling with water. This makes the up-stroke lighter.
Now for the details:
At the upper end, the only complexity is that a 1-1/2″ by 3/4″ bushing must be reamed out in order to allow it to slide freely over the 3/4″ central rod (pipe). This bushing must not be glued in place, as it forms the guide bearing for the motion of the handle, and also is required to pull out of the top tee of the pump casing in order to open it for maintenance. All the other joints shown in the upper end photo, can be glued.
Otherwise, it can be made, as illustrated here, from a 1-1/2″ PVC male pipe thread adaptor (MPT adaptor), a threaded end cap, a disk cut from automotive inner tube rubber, and a 3/8″ by 1″ bolt with nut and washer. The cap is drilled as illustrated, and the disk of rubber is securely anchored inside with the bolt so that it covers the holes around the periphery, loosely.
The present version of the plunger has been made a little more efficient than earlier versions, by using a 1/2″ by 2″ bolt and two 1/2″ nuts, to secure it to a 1/2″ MPT adaptor, as shown. This allows a sufficient annulus between the nut and the inner wall of the cap, to drill the perforations needed for the water to pass through the plunger on the down stroke. The plunger can be made from a 1″ PVC cap, sanded down slightly to fit easily into the 1-1/2″ cylinder, and drilled as shown here. The central hole is 1/2″ diameter to fit the bolt. The disk of inner tube rubber rests on top of the plunger and acts as a poppet valve to allow water to flow only upwards through the plunger.