We've had a few members open up the speedometer, and repair the odometer, it all comes down to gears not secured to a common shaft, a dab or two of adhesive usually cures the problem .
The bouncing speedometer needle, is caused by a 'dry' drive cable, try putting a light oil down the cable, from the speedometer end, and see if it cures the problem .
Worse case scenario, you need to replace it .
I've been cleaning and lubing mine for about the last 25 years .
I make cleaning and lubing the drive cable, part of the yearly maintenance that gets done in November, when it's safe to go into the garage, without fear of heatstroke .