I used to get speedo bouncing on an old european daily driver on very cold days. It was concluded to be the speedo cable (a very long narrow spring inside a sheath) that was binding slightly and would spring back when it freed itself causing the needle to bounce.
Julian's test is a good one. Lubricating the cable properly (if it's not a sealed cable) and avoiding any kinks in the cable path is the most likely cure.
Mark
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