The songs starts with a city-wide search for the speaker: "All over town, the question is going 'round/ 'Where, oh where, can he be?'"
The reference to the old song "Where Has My Little Dog Gone?" leads us to understand that they are searching for him out of concern, and that this is not, say, a manhunt for a criminal.
However, he is not hoping for rescue, either. He is, in fact, just looking for a place to be alone to mope. "I'm hiding in the chapel... You ask me why I sit here and cry... Oh, Lord above/ The only girl I love/ Has gone."
Even though he is not a criminal, he is using the chapel as a sanctuary of a similar sort. Mostly, he is hiding from the concerns, blandishments, and cheering-up of others. He is sad, and wants to be sad. And, just as a wounded animal does, he found a safe den in which to lick his wounds, so to speak.
In a way, he is also signaling those who search for him that he is in severe emotional pain. If he were mostly fine, he would seek their solace and allow himself to be comforted.
Also, he is hiding, he says, "from a broken heart." Something about the chapel allows him to feel distracted.
The next line is somewhat melodramatic: "Here I'll stay, until I hear her say/ That she wants me back again." This is passive-aggressive, but also typical behavior for a wounded person. Probably, he will stay until he gets hungry enough to leave.
Up to this point, he has imagined that his lost love has done one of three things-- moved on, mourned the loss of their relationship, or joined the search for him in order to take him back.
Then he realizes, or has somehow heard (unlikely, as who could tell him?), a fourth possibility: "If it's true that she is hiding, too..."
She might be pulling the same stunt he is! In that case, "I'll search for her." Well, he has put himself in a Catch-22. He is willing to seek her out of she is hiding, but cannot know if this is the case since he is hiding!
It would be easy to deduce that the speaker is disturbed. More likely, he is freshly hurt and simply seeking a place to be alone with his thoughts-- and the Lord. His behavior in this sense, is rational in its irrationality. Of course he's not making sense; his world has just been upended!
There is an assumption that someone sad needs to be cheered up. But sometimes, it's important to just be sad, to have the feeling fully, and let it subside on its own. Attempts to suppress it will only cause it to fester and build up pressure until there is an outburst.
Our speaker is in mourning, a legitimate and perfectly healthy reaction to heartbreak. He will get better, and sort his conflicted feelings out. At least he knows that he needs privacy and solitude in order to do so, and has the wisdom to seek out a place where no one will look for him, so he can recover in peace.
NOTE: This next series of songs is not available, as far as I can discern, online. They are on parts 2 and 3 of a series of 3 CDs collectively titled "Paul Simon aka Jerry Landis: Work in Progress." The subtitle most likely refers not only to the songs but to Simon, as they predate his Simon and Garfunkel output, and so present--to borrow a phrase-- a portrait of the songwriter as a young man. It is an excellent series, with very good biographical and discography (discographical?) information.
Next Song: The People in the Story