Sounds like either the little dowel that connects this gear position shaft (5) to the selector drum (4), or the spring and/or pin (6, 7) is missing/broken/not working.
When the selector drum is rotated, the gear position shaft rotates with it, and via pin (7) it touches various spots on the gear position sensor (GPS).
On 08/10 and newer Rocket IIIs the GPS has the pin built in so no need for the pin and spring.
This is how the gear position shaft rotates;