If everyone could just look CLOSELY at where President Kennedy's hands go to...
The hands are never at "neck level", they never go near the throat, and he never "clutched his throat". Sadly, this entire idea seems to stem from no one having made blow ups of the Z frames for a cursory examination of the film to examine exactly what happened, before 1966 when John Connally examined blown up frames trying to determine when he was shot. Life Magazine is responsible for claiming that the President "clutched his throat" in its October 1964 edition, in one of the captions for the Zapruder frames they published in that issue.
The right hand is the first to go into position in a cupped fashion, over the mouth. The left hand comes up, every finger except for the index finger are curled. The index finger is slightly curled but in a near straight position as the hand forms into a semi-fist and comes up against the bottom the right hand. It looks like he could very well be dry heaving after the bullet that ripped through his back exited the throat. As he starts to turn his head to his left, his right hand--now in a semi-cupped position-is now at cheek level as his head turns and the hand remains in the upward position. He doesn't start to bring the left hand/arm down until after Mrs. Kennedy grasps his left arm and pulls him slightly downward and toward her. His right hand then moves from cheek level down to chest level where it remains until the fatal shot is fired.