A character has red eyes, but they do not really signify a certain trait.
Enforced: "Let's give the Big Bad red eyes so he can be identified as the villain."
Lampshaded: "So you're behind this all? I should have known since the moment I looked in your evil red eyes."
Invoked: Albinism is fairly common in the setting. The Big Bad spreads a rumor that any child with the trait is destined to become evil; that way, he ensures that he will always have a supply of hated and feared minions with nowhere else to go.
Exploited: Prince Strongheart needs to pass for evil, so he gets himself a pair of red contact lenses.
Defied: "My eyes may be red, but my heart is pure!"
Discussed: "So, are red eyes a requisite for villainy?"
"Why do such a high proportion of evil-doers have red eyes?"
"He must be the bad guy. Just look at those eyes."
Deconstructed: Lord Bloodstone was hated and feared ever since he was a child because of his sinister-looking eyes. The abuse he suffered twisted him into the villain that he is today.
Reconstructed: Lord Bloodstone was hated and feared ever since he was a child because the power of the Demon King that dwells within him, and people felt inherently afraid of him. As he grew more twisted and bitter, his eyes became redder, a sign of the Demon King gaining control. The hero has the same power, but maintains his heroic nature, and so his eyes are an untainted blue.