First, I verified the dispenser motor was working by removing the ice bin and marking the top of the drive shaft with a Sharpie. After closing the freezer door press the Ice button briefly on the Cubed setting. Then open the door to see if the shaft marking has changed position. Do the same for the reverse direction, or Crushed setting.
When my new drive shaft arrived with the coupling sleeve already attached. I could see very quickly that my original drive shaft coupling sleeve had slid upwards, meaning the original drive shaft had dropped such that it no longer engaged with the ice bin.
Of course, all that was necessary to fix my issue was to either move the drive shaft coupling sleeve back into the original position or replace this drive shaft coupling sleeve.
A new shaft was not required here, as the drive shaft coupling sleeve is sold separately.