Does anyone know the solution to a bouncing speedometer needle? Is there an easy fix or does it have to be rebuilt.

 

Most likely it's the cable. As they get old and dirty the inner cable can bind as it turns making the needle jump about. You can often just remove the inner cable (pull it out from one end or the other) and carefully wipe it clean. Don't lubricate it with oil or any liquid lube as it will just end up binding again, rather lightly lube the inner cable with graphite (like locksmiths use on lock tumblers) and carefully roll it as you put it back in the outer cable. There's a good chance that will fix your problem.

 

I second what Irgridley said. I have fixed several bouncing speedo that way.

 

Could be cable, but in my '69 series2 it was some sort of magnetic feed in the speedo itself, and had to get the speedo sent off and fixed. Had it calibrated at the same time. Works great now.

 

The speedo is a very simple device. My problem resulted from seized counter mechanism. I loosed this and the problem went away.
another problem developed when I had the gearbox rebuilt. I believe the mechanic damaged the angle drive when he removed engine.
Within the drive is a short flexible drive. It had detached and been pushed in by hand, this caused intermittent contact and a very jumpy needle.
the Angle drive is exceedingly difficult to get to.
My 69 had had a very neat hole cut into the tunnel which aided replacement. Without it I could not see how it would be replaced.