ToyMotor replied:

My 60 was the same, I never fixed it, but I reckon you'd need to change the outer, as the bouncing is probably the inner "winding up" where the nylon sleeve is worn away in the outer. It's pretty easy to access the speedo end, by taking out the screws holding the instrument panel in, the panel comes out far enough to undo the cable. (I got it down to a fine art repairing the tacho about 4 times)

Cheers

Well 55 replied:

Yep you have gotta replace the lot, when you do make sure you put a new "O" ring at the gearbox end, so as not to get a oil leak latter on.

bill replied:

When you undo the cable from the speedo, tie a piece of string to the cable before you pull out the cable, then pull out the cable, tie string to new cable and gently pull new cable thru the rear of the heater assembly otherwise it's near impossible to find the cable once you put it thru the body and you save a lot of time