Does anything look amiss here? Every time I open it, it's not 'in position' and changing gears doesn't move it until I rotate it into the proper position.
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.
Success! I trimmed it a bit and it shows it's in neutral and will start with the kickstand down. Popped it into first and the bike cut out like it should with the kickstand down.
After taking it for a spin and filling up the tank, the only thing wrong now is the broken speedo. I've been using a phone mount and a speedo app for now.
I've seen a few of the threads about aftermarket gauges, and I think I'm just gonna let a shop deal with it. One full tear down and rebuild is more than enough work for me.