The Button Eye is an eye from Cell Stage and early Creature Stage. Strangely, none of the starter cells have this eye.
Cells with this eye include: Goldy, Bloato, Jawhead, Buzzy, Needle Buzzy, Jetster and Snorf.
Creatures with this eye include: Kroon, Doofnit, Squee, Hivehat, Jayel, Tuunk, and many more.