Did a little experimenting with a head control based on an illustration in Rod Puppets and Table-top Puppets by Hansjürgen Fettig. I really like the smooth movements the thumb control has (helped in part by press fitting a short piece of brass tubing in the control to act as a bushing.)
As you may be able to tell from the video, the original plan was to control it turned around 180 degrees. The little semi-circle cut was to rest your thumb in. In that position, though, moving the thumb pad down makes the puppet look down. This seems like it would make it more intuitive, but since you're controlling from the back end of the rotational point left and right motion is reversed. It seemed weird to me, so I just flipped the head around and operate it backwards.