eye mechs and such
I know there were several drawings of things like that on the forum. While it's not muppets try searching for Figuremaking can be Fun. It is aimed at making Ventriloquism mechs, but the operation is similar. I also think Puppet Planet had a dissection of an old Fisher Price 'Animal' puppet that shows how the blink works.
As far as Beaker goes, I believe they built different Beakers for each possible eye movement/feature. There's only so much space in the puppet's 'skull' for these mechanisms to work and still have room for the hand or other controls.