I do this sort of work professionally. I'm an RV Service Tech at a Gulfstream dealership.
Your system is obsolete, as many are.. . See this link:
https://www.gulfstreamcoach.com/medi...tem-Manual.pdf This is your system I'm pretty sure. Meaning the jack is either DN12581 (2.5" BORE, gas coach) or DN12989 (3" Bore, diesel coach).
There are rebuild kits out there similar to this:
https://www.amazon.com/Power-Gear-35.../dp/B06Y61D3CQ
But with some searching you might find a new cylinder to replace the old. It's double action, so after you swap it out, over extend it each direction, and continue running the pump (hold the button) to pump air out. Wait a few minutes each time you do this (in fully extended/retracted position). Check reservoir fluid level with all jacks up.
As others have commented, there are hydraulic shops out there that can rebuild the jack . . . Issue being it is hard to find the right (size) seals.
BTW, don't overtighten the hydraulic fittings.
Hope this helps a little.