Jeff, I just realized that I made an error on the earlier post (memory's fading as I get older, I guess /forums/images/graemlins/frown.gif). My pneumatic grease gun was a "Versital by Alemite" not a Lincoln. My last big manual gun was a Lincoln, I think.
Anyway, I've not seen one react as you say your Lincoln is doing, and I don't remember model numbers well enough, but isn't your gun one of those on which you can pull and hold the trigger and it keeps pumping until you release the trigger? We used those types in Dad's service stations when I was a teenager, but of course they were connected to a barrel of grease. The one I had that used the tubes of grease would only pump one stroke when you pulled the trigger. You had to release the trigger and pull again for the next stroke. I didn't like that quite as well, but since it would pump as fast as you could pull, release, pull, release, etc. I didn't have any complaints with it. I bought it at Tractor Supply Co.