I wish there was more to say, this question was inspired by this image. Now I know that they are robots but is there a way that I could achieve glowing eyes in real biology?
Maybe they mimic a species of bioluminescent prey animals who attract mates with light. So the eyes evolved to lure in food. If the chemical that luminesces is produced by the brain, then maybe it isn't just their eyes that glow, but their entire brain. The eyes are just the only place where the light can shine out, and the glowing brain became a survival positive trait when it started attracting food.
It gives them an advantage in hunting food. Anglerfish have bioluminescent protrusions that attract prey and mates. Glowing eyes are definitely not beyond the realm of possibility since, as @Aify points out in the comments, exist in some animals.