I had the same problem with mine a couple of years ago. Fortunately, my dad worked on this stuff in the 1950's and he knew exactly how to fix it. Problem is, I wasn't watching too closely when he fixed mine, and he passed away this spring. I want to say he did add a drop of oil and kept testing the needle by turning the needle and finally it was consistent returning back to its proper resting position. He must have played with the needle a hundred times until it was returning consistently. Mine is still off by 3-5 mph, (+ new speedo cable) but I can live with that, at least I have a pretty good idea as opposed to hoping their wasn't a Kojak with a Kodak hiding behind a tree. Good luck, keep playing, and if you break it, then pick one up on e-bay. Lol.
Wada