I recently made a puppet with a big furry unibrow thingy that sort of doubles as a uni-lash. It's a really simple way of creating a very expressive blink type effect (take a look at marvin in "the sit-in" and "the last show" episodes of the itche kadoozy show.) All it is is a piece of hanger bent into three sides of a square. Poke a hole through the head on the outer sade of each eye. Put the hanger thing inside the head and poke the two ends through the holes. Now bend them around the curve of the eye, or just bend them and the corner at a 45 degree angle. Glue your eyebrow.eyelesh thing on there. If you go with the slant (instead of the form-fitting curve) it creates a happy or surprised look when up and an upset or angry look when down. If the fur is shaggy enough it'll cover the eye enough without an eyelid, but I guess you could go for a lid if you want. The straight bar on the inside gives you a really stable and simple trigger than can be used by any finger that's available (not just the middle).
Hope that helps.