In The Great Gatsby, what is the significance of the "owl-eyed" man?

This minor character contributes to the motif Fitzgerald introduces early in the novel through the presence of T.J. Eckleburg and his huge eyes on the billboard in the Valley of the Ashes. Like the inanimate Eckleburg, Owl Eyes acts as an impartial observer of events. Unlike Eckleburg, Owl Eyes does make a final moral judgment of Gatsby's life and death.

It is through his character that we learn Gatsby's library is full of books that are real, if unread. Owl Eyes is amazed.  For the reader, Owl Eye's discovery suggests Gatsby's wealth and the detail in which he constructed his new identity in order to impress Daisy. This incident gives us another insight into Gatsby's commitment to his dream.

The real significance of the owl-eyed man, however, is found in the novel's conclusion when he suddenly appears at Gatsby's funeral, one of only a handful of people who attend. His presence itself suggests moral responsibility in his character: He shows up. He also apologizes to Nick for not paying his respects at Gatsby's home. Owl Eyes is someone whose opinion deserves our respect.

It is he who recognizes and acknowledges the tragedy of Gatsby's life and destruction. Owl Eyes wipes the rain from his glasses. Seeing clearly, figuratively as well as literally, he pronounces Gatsby's benediction: "The poor son-of-a-bitch." With this, impartial observation becomes moral judgment and the novel's themes are further emphasized.