What he said was that he never turned around far enough. And we can see in the Zapruder film that he didn't. Dale Myers has Connally turning sharply to the right beginning at Z157 and reaching 48 degrees of right rotation at Z193.
He did not say the never turned around far enough. His WC testimony indicates that he turned as far as he could but could not catch the President out of the corner of his eye:
"I heard this noise which I immediately took to be a rifle shot. I instinctively turned to my right because the sound appeared to come from over my right shoulder, so I turned to look back
over my right shoulder, and I saw nothing unusual except just people in the crowd, but
I did not catch the President in the corner of my eye, and I was interested, because once I heard the shot in my own mind I identified it as a rifle shot, and I immediately--t
he only thought that crossed my mind was that this is an assassination attempt.
So I looked, failing to see him, I was turning to look back over my left shoulder into the back seat, but I never got that far in my turn. I got about in the position I am in now facing you, looking a little bit to the left of center, and then I felt like someone had hit me in the back."
It is absurd to suggest that Gov. Connally was in any way attempting to see JFK prior to disappearing behind the sign and absolutely no suggestion by his actions that he was consumed with fear that an assassination attempt was unfolding. All of that occurs after he reappears from behind the Stemmons sign.