I found out about this forum too late for help. So I'll tell you what I tried and it worked. 1st. I've had this old Southwest pump for 21 years and use it often to fill lawnmower, tiller, and put in gas cans to mix 2 cycle oil. It started working in just 1 direction of the handle so I took it apart and found leather cups were bad on one cylinder and was very thin on the other and they would have broke shortly. Couldn't find leather cups or pump shaft packing on any site for visible gas pumps. I checked at a place that repaired windmills and the had exact size of cups but no packing. For packing I bought 3/8" nylon rope and worked wheel bearing grease in it good and used it for packing. Put it all back together and it works perfect.
Why couldn't I find these parts on any site for these old visible gas pumps.
Pump photo attached
