Hello. My name is Michael. I can help you with your question.
Based on the Paider patent and the diagrams included in it, it appears that the reservoir is 10a on the diagram - middle right. Leading into that:
Below the piston 10, there is a hollow plug 15 threaded in the pump chamber which is closed at its bottom by a suitable cap 16 in threaded relation with the walls of the pump chamber. It will be noted that the plug 15 has a central passage 15a that terminates in an upper valve seat 17 and a restricted inlet port 18 at its upper end. Upon the bottom of the plug 15 there is a perforated plate 19 and upon the bottom of the piston there is a perforated plate 20 which extends over a recess 21 in the bottom of the piston that terminates in a valve seat.
So, I believe that is the fill port. It is difficult to know for sure from the patents, especially since this is from at least a decade before your chair. But it's not documented anywhere, so this is a start.