Bob,
I will be refering to the pics that you posted this morning. In pic #1 you can clearly see the coggs (or dogs as chuck K probably correctly called them), right at the base of the spindle drive pully. At about 12 o'clock, and 5 o'clock the lighter dogs are part of the pully, and the darker dog in between them is part of the handwheel, which is keyed to the spindle. When the dogs are meshed together, as in pic #1, the spindle (and handwheel) turn at the same speed as the drive pully. When you pull the handwheel out, then engage the backgear, the spindle, and the handwheel (remember it's keyed to the spindle) turn much slower than the drive pully. So, you need to put oil in that capped oil hole at 12o'clock on the face of the pully (still pic #1), for every 8 hr. of backgear operation (I do it much more offen). One more thing, there is a ball and indent of some type that holds the handwheel in either the meshed or unmeshed positions, so no pin is needed.
Now back to your problem, I would drip some penetrating oil in between all the dogs, and in the pully oil hole (the cap unscrews) that I mentioned above. Then, most importantly, you MUST pull very straight with 2 hands on the handwheel. The bushing is a very tight slip fit on the spindle, Mine moves easilly, but if i try do pull it from only 1 side, it binds and wont budge.
Now, for pic #2, I have to assume that because the pic is looking so straight at the spindle, I can't see that the spindle sticks out past the handwheel by a little bit, as seen in pic 1. Or did you remove something? If you put your finger on the OD of that round spanner nut, and slide finger in a little, you will feel that there is a small gap between the inside of the nut and the outside base of the handwheel. When you pull on the handwheel it moves the distance of that gap and stops against the nut
OK, I just re-read your second post. If that part that sticks out further than the handwheel is a sleeve than that explaines why, with my collet closser (yes that pipe in 2nd pic of 2nd post is the collet closer) the pipe seemed to be too long. I didn't have that sleeve. You can unscrew it if you want, but be sure and keep it with the rest of the collet closser parts. But even if you leave it on, it wont interfere with slidding the handwheel out to dissengage the spindle.
Anyway, sorry, this is soo long, I felt that if you know how it works, then you will see that there is nothing keeping the handwheel from pulling out, other than probably old dried out oil or grease. It may not have been mooved for many many years. I am including 2 pics of my "backgear handwheel". First one, dogs engaged with pully dogs (like yours), Second pic, handwheel pulled back so disengaged from pully, and lathe ready to be put in backgears. Hope this helps, JR49 EDIT, Don't know why pics got on top of my post, or why there are 2 of the disengaged pics. Oh well you get the point. Good luck