Oswald's Team

 This is partly best guess.

Oswald was an FBI informant, and a CIA asset.  He was infiltrating opponents of Kennedy to find out about plots.  He warned the FBI about them and got no response.

The book depository was one of several different angles Kennedy could be shot from.  The very idea of such an assassination is to have so many angles that certain people can be the patsy for others, usually ending up blaming the assassination on some lone nut.

But Oswald wasn't a Lone Nut, he was married and an FBI informant.  The group of people he had infiltrated included mob people under Jack Ruby.  They were going to shoot from the book depository.  Oswald himself wasn't considered good enough, but there were going to be others.

They never showed up.  They were to be there an hour in advance and set up.  Oswald knew they could not set up in a few minutes.  At noon he gave up, waiting in the kitchen where he could see people going in and out of the back door just in case.

But unbeknownst to Oswald, the mob sharpshooter had joined the CIA team behind the grassy knoll  When Jack Ruby took a look out the depository window he said no way in hell we're going to make that shot.  So instead the Book Depository was occupied by professional military snipers.  They rushed in the other door when a diversion was created on the street, bypassing Oswald.

Was Kennedy hit by CIA or mob behind the grassy knoll?  The most likely CIA, E Howard Hunt said it was someone else, but he was part of the same group of shooters (in his alleged deathbed confession to his son, facts he had denied all his life).  A friend of mine doesn't think even the grassy knoll shot is easy enough except for intelligence or military snipers, but I'm not so sure.  The book depository shot is harder still.  I guess the mob guy got lucky, at least until caught for something else later.  Even the military had hard time from Book Depository window.

Oswald could identify the mob people involved, but strangely (to Oswald) nobody asked that.  The job was to stall until Ruby himself would dispose of the matter, thus revealing nothing to anyone.