The absolute minimal conspiracy: Someone in a high place of authority , found out that Oswald was a defector , a Marxist who had gone looney tune, who had ordered an MC rifle and a revolver using a fake ID, and that he had taken a shot at Walker. The conspirator found out that Oswald had a job in the TSBD.
The conspirator found a CIA psychological profile of Oswald that indicated he was a volatile unstable personality with delusions of grandeur.
The conspirator figures all he has do is to ask that the JFK motorcade route be slightly altered so that it would go past the TSBD building owned by his good friend, Harold Byrd. Probably some story given that Byrd really admired JFK and that it would be an honor for his working class employees to be able to see and wave at JFK up close.
Then the conspirator rides in the motorcade because he reasons that if he does not participate , his absence will be suspect when JFK gets shot. So the conspirator rides in a car just far enough behind the JFK car not to be an immediate target, but close enough to be able to see the TSBD windows when the JFK limo
turns on Elm st. At that point the conspirator ducks down in his seat just to be safe, as he waits to see if the Oswald Kook that the CIA profile predicts will likely act will assassinate the conspirators no.1 most hated political rival: JFK.
Afterwards when the conspirator becomes the President of the USA, he will use the same method to dispose of Malcolm X, MLK, and RFK.