Final answer:
The vagus nerve, or tenth cranial nerve, innervates several major organs in the thoracic and upper abdominal cavities but does not have functions pertaining to pupillary size control, salivation, or taste sensation.
Step-by-step explanation:
The vagus nerve, also known as the tenth cranial nerve, is responsible for the autonomic control of organs primarily located in the thoracic and upper abdominal cavities. Therefore, any structure outside of these regions would not be innervated by the vagus nerve. Some of the key structures innervated by the vagus nerve include the heart, lungs, esophagus, stomach, liver, pancreas, gall bladder, and small intestine.
The dorsal nucleus of the vagus nerve is the origin of these parasympathetic fibers that project through the vagus nerve to terminal ganglia in these cavities. It's important to note that the vagus nerve does not innervate muscles of the eyes or control pupillary size, that function is served by the oculomotor nerve (cranial nerve III), through the Edinger-Westphal nucleus and its connection to the ciliary ganglion.
Similarly, salivation is controlled by the facial and glossopharyngeal nerves that originate from the salivatory nuclei, and not by the vagus nerve. Taste sensation is also not a role of the vagus nerve, as it is relayed to the brain stem through the facial and glossopharyngeal nerves.