While removing the throttle wheel from the stick unit I noticed two small plastic rings connected by a spring jumping away. It took me quite some time to figure out the correct position when assembling the stick. In case you encounter this problem too, this is how the rings have to sit on the throttle wheel:
The next Saturn peripheral on my list is the Sega Mission Stick.
This is the black US model MK-80104:
It has been used before but is still in a very good shape. Unfortunately it smells rather strange. Better take it apart to give it a good cleaning.