Why does Fitzgerald have the Owl-Eyed Man attend Gatsby's funeral? What might he represent?

The owl-eyed man is an observer, someone whose clear-sightedness allows him to see Gatsby for who he really is. We first meet him in chapter three: He claims to have been drunk "for about a week," and he looks at Gatsby's library in astonishment:

“Absolutely real — have pages and everything. I thought they’d be a nice durable cardboard. Matter of fact, they’re absolutely real. Pages and — Here! Lemme show you.”

Taking our scepticism for granted, he rushed to the bookcases and returned with Volume One of the “Stoddard Lectures.”

“See!” he cried triumphantly. “It’s a bona-fide piece of printed matter. It fooled me. This fella’s a regular Belasco. It’s a triumph. What thoroughness! What realism! Knew when to stop, too — didn't cut the pages."

David Belasco was a famous Broadway producer, known for the realism of his stage sets. The owl-eyed man correctly sees Gatsby's house, and his party, and possibly his guests (Nick included?) as stage props.

When he comes to Gatsby's funeral, he says a few words to Nick:

We straggled down quickly through the rain to the cars. Owl-eyes spoke to me by the gate.

“I couldn’t get to the house,” he remarked.

“Neither could anybody else.”

“Go on!” He started. “Why, my God! they used to go there by the hundreds.”

The owl-eyed man's sympathetic feelings for Gatsby are a little confusing if we think of him as impartial. I think far from being impartial, the owl-eyed man is maybe the only character in the book who is able to fully empathize with Gatsby. His appearance at the funeral allows Fitzgerald to give his pithiest assessment of Gatsby's career ever:

He took off his glasses and wiped them again, outside and in. “The poor son-of-a-bitch,” he said.”