Graves claims to know what Gov Connally was thinking too. His claiming that Connally was turning to his (L) in order to check on Nellie is pure fabrication.
Comrade Storing,
Why did Connally quickly turn far to his right around Z-140, quickly turn to his left around Z-154, quickly turn far to his right around Z-168, and start turning to his left again (when he was hit by CE-399 at Z-222)?
Answer: Because he heard the loud sound "behind and to his right" at "Z-124" and recognized it as a rifle shot.
Regarding why Connally turned quickly to his left around Z-154 (and was captured looking straight ahead by Croft at Z-161), it was Charles Collins' idea that he did so to see if Nellie was okay, and Charles points out the JFK turned his head towards Jackie right before that.
If you have a problem with that, take it up with Charles, not me.
-- Tom