I was lucky to figure it out by chance.
The mechanical plastic gear replacement worked well.
The problem was the step motor not working.
I tried to gather information about the electronic part of the odometer and found some on the German web.
https://www.w126-wiki.de/index.php?title=Tachometer_reparieren
The most useful piece was the description and the circuit diagrams.
I could understand how the tachometer/odometer is working:
the signal from the transmission is rectified and cleared by the electronics and driving the 3 coils... 2 for the step motor and 1 for the tach.
Then I found that the board was repaired before as there were rougher solder points and I figured out that someone had disconnected the board (from the hardware). Then I found that the small vertical circuit board (blocking the access to the gear cover) that described yesterday was removed and soldered back as well.
Then I found that the one of the 4 pins was not soldered correctly and the pin was lose. So I resolved that pin and put the instrument back together and
voila.... it worked again.
I'd say I was clearly lucky having found this information on the web.
I am showing some pictures from the board and the pin connection and the plug
I hope that this information can give some people support at a later time when they are in need.
Martin