Final answer:
Abnormality in a patient's left pupil accommodation likely indicates a problem with cranial nerve III (the oculomotor nerve), which controls eye movements including pupil constriction and accommodation.
Step-by-step explanation:
If a patient's left pupil fails to accommodate, this finding may reflect an abnormality in cranial nerve III, also known as the oculomotor nerve. This nerve is responsible for controlling several functions of the eye, including pupil constriction, dilation, and accommodation. The accommodation reflex involves the ability of the eye to focus on near objects by changing the shape of the lens, and this process is governed by the oculomotor nerve.
The oculomotor nerve contains preganglionic parasympathetic fibers that originate from the Edinger-Westphal nucleus. When light is shone in one eye and only the opposite pupil constricts (consensual reflex), but not the direct pupillary reflex in the affected eye, this suggests damage to the oculomotor nerve on the side without direct pupillary constriction. Therefore, if a patient's left pupil does not respond to light (accommodation or direct reflex), it suggests damage to the left oculomotor connections, indicating a potential abnormality in the oculomotor nerve on that side.