So... I built Max and was on the crew that went to Norway for the filming of the space ship interior. Yes, Norway! But that's another story.
There was basically only one head with a bunch of spare parts. Most of the shots had a frosted "eye" sphere with fiber optics and I think a few incandescent bulbs to light it up. For a few shots we used a "coherent fiber-optic bundle" which was a bundle of 25,000 optical fibers that could be used to rear project images onto a spherical rear-projection screen inside the head. This would allow, in theory, for the flexible bundle to be run down the jointed arm from the ceiling so the Max puppet could be moved around the set while images were projected inside the eye. In practice it turned out to be more trouble than it was worth to shoot and was used very little.
I might have some photos from the build/shoot somewhere. No promises, but I'll dig around.
Your model is looking great!