Searching on "exact and similar matches" for John and "exact, sounds like and similar" matches for Fitzpatrick didn't lead me to my great-uncle's birth certificate. Even changing the Fitzpatrick surname search to "broad" and then trying John and Fitz* didn't help.
I started to think that his birth wasn't recorded, or that he was actually born before 1906, or maybe even in a different state. Then I decided to search for just his parents' first names, Charles and Eva. Success! My great-uncle's name had been transcribed as John Gaelord Filzfadrick.
Transcription errors are unfortunate and make it very difficult to find ancestors, especially if we don't know where and when they were born. However, if we think of different ways to search for them, sometimes it often leads us to the records we're looking for. (And submitting corrections will help those who may search for the same person later.)