The Peeper and Oculus from Subnautica, with a hollow eye just big enough to fit a CR2032 battery with some little LEDs on the sides.

First plate is the Peeper, second is the Oculus, and third is the battery holder. To put it together, I wrapped two pieces of copper tape around the flat surface starting on an inside to get the + and - on either side of the battery. From there I soldered on a 5630 LED on to each side (anything similar should work as well, I just found these in my light drawer first), slid the battery in, and tried not to blind myself. Place the battery assembly along with the 3 little pin things on one half of the body, than snap the other over top and you're done. How do you turn it off? Well, take it apart and slide the battery out. I wasn't smart enough to figure out how to integrate a switch in yet. Oh well.

To anyone more well versed in electronics than I am (i.e: anyone), please let me know if there's a better way to get LEDs on the side of a CR2032 than this, I'm sure there is, but what I did worked so it's good enough for me.

The light sits conveniently behind the pupil, and will light up the lighter iris around it to get that nice ambient glowing effect like in game. Well, the Oculus at least, I don't remember the Peeper's eyes glowing, but hey, why not? The glow effect will be a factor of the filament used and infill, so that may require some tweaking from my profiles to get your desired effect.

If you don't want to deal with the LED, just glue the two halves together, you don't even have to remove the supports! Though you really don't even need them if you intend to glue it together.