Hi Shawn, not too complicated on the PVC half sphere. Just  like a ping pong ball cut in half, but they are stronger, and you can make them the size, and to a degree, the  shape you want.. and pretty much for free.
   Here are a couple pics of the eye closer up for you to  study, and hopefully an understandable diagram of proceedure. Not too complicated once you have done it once.

      

Got it... I thought maybe that was what you meant but wanted to clarify.  Thanks for the details.

Is the eye sewn just to the tube from the back rather than the head fabric on the front?  I wonder if the tube extension could be used to move the eyeball independently in the socket if you could find a way to keep the ball pressed against the head skin tightly. Then your "mule" could go cross eyed while he wiggles his ears.

Yes Snail. At first I did cut a slit in the foam as well as the cloth,for the cloth tube to go through, and had a  wooden ball, which could lend itself towards a moving mechanism, but since it was a 'draft' puppet, I went simpler and just did the half sphere covered, and hand stitched from the front. You have given me some food for thought.... I feel something coming on.

Good idea Sail! It would be a bit like a ball and socket joint then.  Hmmm...

yes....a half sphere PVC socket with a wooden ball moving  in that with a stick on the back to move it....then could one get the eyelid to blink? hmmmm.

Hey Shawn I did a tutorial on the PVC half speres. I posted the vid link in the  'Eyes - Feedback Please'  thread.

Cool!... I'll have to check it out when I have more time.

By the way, the horse was used day before yesterday in a end of semester school production, as the kings horse in Beauty and the beast. Not a puppet as such, but got used  anyway.

Neat! Did you make a body for him or was it a stick horse?