① First Appearance: Library. In this scene, the Owl Eyes man fervently exclaims that all the books in Gatsby's possession are authentic. Up until this point, all the guests at Gatsby's party have made (outrageous) speculations about him. Despite Nick and Jordan's dismissal of his claims, he brings to the table a very few very important questions: How rich is Gatsby? How authentic is he? This brings to light just how particular this Gatsby character is; unknown at his own party and the only truth we discover is that he has actual books. This tidbit of information ciments a reality to the identity of Gatsby; he isn't "empty" like the rest of the people that attend his party.
② Second Appearance: Car crash. After Owl Eyes loudly proclaims that he is finished with the whole business; it is not clear (either to Nick or to the reader) what, if anything, he means by this. Owl man claims he wasn Gatsby's party, there's this bizarre car accident that Nick just happens to stumble upon. 't even the one driving. This is, true or not, is one of the truths (later supported by Jordan) that people tend not to take the blame for things they do.
③ Third Appearance: Gatsby's Funeral. Essentially, there are only three people who attend this event of mourning: Nick, Gatsby's father, and Owl Eyes. And of all the people that partake in the Gatsby's grandeur displays of wealth, only said three people made an appearance. It's obvious why Nick and Gatsby's father showed up, but what is the importance of the Owl Eyes' attendance? Disappointingly enough, the people who show are the people who took time to learn of Gatsby; rather than making and spreading incredulous rumors about the mad. In which, one can say that the third truth is that not many bother to look underneath the extravagant displays of wealth. Perhaps Fitzgerald is trying to drive home the superficiality of the people in the roaring twenties; heck, this can be a general statement targeted to the lot of human kind.