So... You cut the eye template from cardboard, then cut out just the pupil from the inner layer of plastic, and cut the whole eye shape from the upper layer of plastic? Is that right?

How much space is there between the two layers?

Made two plastic copies of the cardboard template for each side, cut the upper one to have a narrow border, then used a strip of the same plastic maybe a cm wide standing at a right angle around the center of the cut-out one. Then glued that to the solid one, went back and added a gusset of hot glue to make it stronger, then cut out the pupil from the back...which probably would have been easier to do before assembly, but it wasn't that hard with a small set of right angle snips.

The black is a layer of fleece wrapped around the edges of the outer part, just 'cuz fleece is easy to work with :)