Welcome to GTt Mike!! Glad you decided to join us!
That pulley never stops spinning, these are not like the old Chiefs where the input pulley has to be stopped to shift,
all that has to stop is the shaft with the brake on it, On the opposite side of the trans.
If you are having issues shifting it could be an issue with the shifter itself or maybe the spring and check ball detents are sticking causing the shifter to not want to move out of (or into ) gear?
If you haven't already I would pull the shifter out and see how it looks, I have seen them bent.And there is a roll pin on the shifter that likes to snap off on one side, causing problems like you are having. You can get a look at the shift forks and rods to see if they are binding.
Just take the shifter off in Neutral so it makes it easier to install after your done.
Also did you check or change the gear oil? These are known to get water in them if they sit outside for years uncovered, It runs right in through the shifter cup.
Good luck! This will at least get you started. I think you may get lucky and find that roll pin broken on the shifter?? Lets hope anyway!!