You might have already solved your problem but I just wanted to chime in. Two years ago this happened to my 66 and it turned out the speedo cable wasn't mated correctly to the speedometer. Basically it wasn't all the way tight. I disconnected it - reconnected it and everything was fine. At any rate, when you get to that stage you'll have access to the cable for cable lube as previously suggested.
Good luck.
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66 Tahoe Turquoise Coupe
Laser Red 96GT Ragtop
Both are slow but easy on the eyes!