Here's my theory:
After having read about an anon's research into the ancient beginnings of their religion, and learning about the story of Athena and Pallus, it seems that it might have something to do with Athena plucking Pallus left eye out during their battle. It might being a symbolic reference to Pallus losing his eye. His remaining eye represents the symbolic eye of Horus. I've also read that in modern times it is "moving up" ritual one goes through where they are given a black eye and expected to "eat the pain".