I had identified the part as Item #8 on the page where the gears are shown.
8 .............. BD920N-2006..........Washer
It didn't seem to want to slide back into place without trying to tap it with something which I found doesn't work cause they are way too brittle.
Gil; OK; So this part looks like a "U" with a grove cut into it? The groove faces out. The part should just slip into the square headed slot on the end of the shaft. These lathes are made to average, but not great, standards. Jet has good tech support so you may want to call them.
There *may* be two shafts where that part is used.
1. The 'a' gear above the banjo.
2. The banjo 120 and 127 gear shaft.
This is one of those situations where the lathes are different between distributors.
(On my Grizzly G4000, the 'a' gear didn't have the 'U' shaped washer, but I fixed that.)
You should not need to turn the shaft to change the gears, just slide the (#8) washer upward to free it and slide the gears on and off.
I would check to see if the bushing/keyway (part #15) is shorter than the gear dimensions. The two gears on the bushing /w keyway should have a sliding press fit. You may also want to back out the shaft a bit to make more space on the shaft. Caution:

Some lathes have a set (grub) screw that locks the 'a' gear shaft in position. The set screw hole is in the edge of the headstock casting. You must back off this set screw before turning the shaft or you will strip the threads on the shaft. AND the set screw isn't shown on the parts lists!
I hope this helps. Work cautiously and think things thru before proceeding.