Sorry to show up so late, but "Second star to the right and straight on til morning" is the directions to Neverland from Disney's Peter Pan. In Neverland, people never grow up, so references to it are usually eluding to a desire to remain a child, to be free of the worries and responsibilities of adulthood and be as carefree and happy as a child would be, forever.
In your example the author is talking about the concept of relative time. It seems to go fast when you're having a good time and very slowly when you're not. Then he says 'like a children's book', which is setting up the Peter Pan reference. I can't tell you more without reading more of the passage, but it sounds like the author is saying that they were searching for someone, perhaps, maybe a person who is dead, and when they were found, the time crept by when the author was in mourning and sailed by when they were engaged in perhaps funeral arrangements or an investigation.
"I flew in and out of weeks and through the years" I believe the author is referring to the feeling that time seems to be speeding by and they are often on auto pilot, only really fully conscious from time to time over the passing years after the subject was found. "Second star to the right and straight on to a morning that will never arrive." I believe the author is talking in double speak. He means that the person that was found, perhaps, will never grow up (because they're deceased) and the happy morning when all this is over will never arrive bc that person is lost forever.
'Second star to the right and straight on til morning' does not refer to time passing quickly at all, under any circumstance. That's incorrect. It's not what the phrase means and it's not what the author meant in this case.