At any rate, here's the UV map for the "Eye_Cover" in case anyone wants to play around with textures for it. (Click for full size)

Yes... I know, it's not designed for texturing in the normal sense, but people are still going to want to be able to, or at least try to.

I have no idea what's up with the missing polys on the UV map at the top and right side, but they're there on the model. Probably a UVLayout map rendering bug.