Owl Eyes was obviously, invited or uninvited, one of Gatsby's guests at one of the ostentatious parties he had at his mansion as part of an attempt to draw Daisy Buchanan nearer. In chapter three, Nick and Jordan Baker were attending one of these to-do affairs and wandered into Jay's 'high Gothic' library where they met this drunk, stout, middle-aged man who was wearing an enormous pair of owl-eyed spectacles, hence Nick's mocking pseudonym for him.
Nick only uses the pseudonym later in his narrative when he mentions an incident when he left the party. On his way out he discovered the man in a car which had had an accident. The car was a wreck and Owl Eyes was the one who stepped out of it, claiming that he did not know what happened, since he had not been the one driving.
The man is mentioned again in the final chapter. He was one of only a few who came to attend Jay's funeral. Nick mentions the following about him:
It was the man with owl-eyed glasses whom I had found marvelling over Gatsby’s books in the library one night three months before.
I’d never seen him since then. I don’t know how he knew about the funeral, or even his name.
The fact that Nick had three separate encounters with Owl Eyes somehow makes him significant. Firstly, he showed remarkable insight when he spoke about Jay and his books. He intuitively recognized that the books were there only for show but that Jay had gone a step further to enhance the illusion, he used real books. Owl Eyes was particularly impressed by the remarkable extent to which Jay had gone to create the impression of class and culture. The books had clearly not been read and he commented:
This fella’s a regular Belasco. It’s a triumph. What thoroughness! What realism! Knew when to stop, too — didn’t cut the pages. But what do you want? What do you expect?
The allusion to Belasco, a well-known theatrical producer, director, playwright and impresario of the period, makes his sentiment quite clear. Gatsby was putting on a show and he was doing it well. His rhetorical questions emphasizes the fact that one could not want or expect less from such a masterful diabolist as Jay Gatsby - the deception had to be perfect.
Furthermore, Owl Eyes links with the huge eyes of Dr T.J. Eckleburg, staring down from a huge road sign onto the Valley of Ashes. Owl Eyes is the personification of what is seen on the large roadside banner. It symbolizes a constant awareness, epitomized by his acute observations in Jay Gatsby's library. In addition, Owl Eyes' observation also suggests that Jay Gatsby is under scrutiny as is illustrated by the countless rumors and gossip surrounding him.
Dr T.J. Eckleburg's eyes, likewise, suggest observation - the world is watching. It is particularly ironic that they should be looming over the Valley of Ashes, a place of physical and moral corruption. It is here that Myrtle Wilson, involved in an illicit affair with Tom Buchanan, lived and it is here that she died - a victim of her, Tom, Jay and Daisy's immorality. They were all, as in Owl Eyes' estimation, Belascos.
A further point is that the observant Owl Eyes is the only one of Jay's guests who attends his funeral. His presence denotes the end of Jay's charade. He was, probably, the only one of them all who saw Jay Gatsby for what he really was. His presence at Jay's final resting place indicates that the scrutiny, the gossip and the rumor has come to an end. Jay Gatsby had, ironically, in the most tragic manner, achieved peace.