In 2014 Conan O'Brien did a spoof of Hillary Clinton's interview with Diane Sawyer about her lack of lingering health issues following her 2012 concussion. In an obviously photoshopped version Clinton's eyes are made to oscillate crazily.
It was a very funny piece. Now, it may not seem so funny.
Hillary Clinton exhibited abnormal eye movements during her recent speech in Philadelphia and they were not photoshopped.
Her eyes did not always move in the same direction at the same time. It appears that she has a problem with her left sixth cranial nerve. That nerve serves only one function and that is to make the lateral rectus muscle contract. That muscle turns the eye in the direction away from the midline.
It comes out of the base of the brain and runs along the floor of the skull, immediately beneath the brain before coursing upward to the eye. Dysfunction of that muscle causes the striking picture of the eyes not aiming in the same direction and causes the patient to suffer double vision.
Like all things medical, there is a long list of potential causes but in my opinion the most likely one, based on Clinton's known medical history is an intermittent lateral rectus palsy caused by damage to or pressure on her sixth cranial nerve.