A zoom stick is a small lever that can screw into the place where the zoom handle is located, it is longer, and allows easier manual zooming. Assuming, that the term "zoom stick" is the correct term. Perhaps I should have used the term, "zoom handle"
Might try finding what thread the holes are on the zoom ring and getting the appropriate size of all-thread and cutting to length. Make a little knob on the end of balled up gaffer tape or a couple of nuts locked together. Never have seen one in the aftermarket.
What the Hec is that? sorry I'm on my iPhone and maybe the picture is not big enough, it looks like a pen sleeved over the original stick! (by the way, I came into this thread thinking I was going to find a stick that would allow me to mount my camera on and zoom in and out with it. lol...)