You're on the right track in that CN VI, abducens, is one of the three nerve that innervate the eye muscles, however CN VI innervates the lateral rectus and abducens palsies are horizontal palsies–the eye is only abnormally positioned on the horizontal plane. When, during the H-test, did the eye not function normally. Was it during horizontal movement or vertical? This image shows the vessels whose occlusion would injure the abducens were it exits from the ventral caudal pons: paramedian branches of the basilar artery. Select another nerve that might be more appropriate.