CN IV, the trochlear nerve, is indeed, one of the three nerves innervating the eye muscles and it involves both horizontal and vertical movement. There are three peculiar things about this nerve. It is the only cranial nerve which exits the brainstem dorsally (seen here exiting from the dorsal midbrain, just caudal to the colliculi). It is the only cranial nerve that crosses sides, and, unlike the others, is not prone to injury from vascular occlusions. In any case, originating from the midbrain, its blood supply would not be branches of the basilar artery. What does cause trochlear palsies are traumatic injuries and congenital abnormalities. Consider the other nerves or return to the case.