The "bounce" can have a couple of sources. It is not normal unless pot holes are involved.
Could be the cable, sticking/squirming inside the sheath. New graphite and light mineral oil should cure that.
...Unless the cable was smashed or kinked at some time. If so, you can examine the inner cable and look for rub marks. Finding these, replace the cable.
Another possible cause is the speedometer itself. The needle is attached to a bell which spins inside (or outside) in close proximity to another bell attached to the drive cable. One of the bells has a magnet which is the coupling mechanism between cable and needle.
If the bearings that the bells ride in get loose, the bells may make actual contact, sending the needle off target at regular intervals. When the bearings get bad enough, the needle spends most of its time at the top limit stop due to friction between the two bells.
Cheers,