[Peter Serio]

The wavering could be a sign that the cable is going bad. I would replace the cable and casing assembly and then road test.

If the pointer is still wavering or your speedometer is reading higher MPH than true the only other thing it could be is the bushing inside of the speedometer is worn and the old oil inside of that bushing has long since turned to glue. Over time the original oil breaks down and once all of the slippery parts of it are gone what's left is more like glue or tar.

What you DON'T want to happen is for the speedometer to lock up. The damage caused when that happens is severe!