The nucleus for the occulomotor nerve (cranial nerve III) lies in the upper portion of the brainstem.  This nerve controls certain extraoccular  muscles and movements.  The Edinger Westphal nucleus is part of the third nerve nucleus, and sends parasympathetic fibers to cause constriction of the pupils.  Through a sophisticated connection of fibers in the brainstem, the occulomotor nerve (cranial nerve III) interacts with the abducens nerve (cranial nerve VI), causing the eyes to move in unison, allowing stereo vision.  Of note is that the parasympathetic fibers (part of the autonomic nervous system) cause constriction of the pupils, while the sympathetic fibers (also part of the autonomic nervous system) cause dilation of the pupils.