I had exactly the same problem on my '87 360. It was
caused by a small gear which which slid to the side on its axle and it got displaced. I just had
to push it back in place (after I got the instrument panel apart of course).
This is the process (from Haynes manual with some steps added), but I take no responsibility
for your actions

1. Disconnect the battery negative lead
2. Remove the covers under the steering wheel and reach behind the instrument panel and
disconnect the speedometer cable (a bayonete type connector which is twisted to release it,
but be careful, you can easily break it)
3. Remove the 2 screws from the top edge of the instrument panel
4. Tilt the panel forward from the top edge sufficiently to disconnect the multi-plugs, taking
note of their location
5. Withdraw the instrument panel from the car.
6. Separate the white part of the instrument panel from the black frame, you will see the
screws
7. remove the needle holding pin at 0 km/h by pulling it out.
8. Mark the position of the needle, then remove the needle by gently pulling it out
9. Remove the front black speedometer plate, held by 2 small screws
10. Remove the speedometer instrument, held by 4 hexagonal screws on the back (around
the speedometer cable connector)
11. You will see the black gear on the top left side (seen from the front). If it's displaced, push
it back to the right.
12. Refitting is a reversal of removal, make sure you fit the needle in the same position as it
was. While you have it apart, you can also replace any blown bulbs.
If that was the problem, you should now be good for another 200 000 km.