Voluntarily tracking an object in the visual field is the function of:

Area 8 is frontal eye field, the area in the frontal lobe that controls voluntary movements of the eyeballs. Vestibular apparatus and vestibulocerebellum are involved in involuntary rotation of eyes that occurs with head rotation. Superior colliculus (SC) is involved in eye-hand co-ordination. SC receives visual input; it sends those signals into cerebellum (tectocerebellar tract). Cerebellum then co-ordinates the contractions of hand muscles. Areas 18, 19 (occipital lobe) -Visual association areas