**Core Concept**
The nucleus ambiguus is a group of neurons located in the medulla oblongata, involved in the control of various cranial nerves, particularly those responsible for swallowing, respiration, and vocalization. Testing the integrity of this nucleus is crucial for assessing the function of these cranial nerves.

**Why the Correct Answer is Right**
The correct answer is associated with the gag reflex, which is a complex reflex arc involving the cranial nerves IX (glossopharyngeal) and X (vagus). The nucleus ambiguus receives afferent input from the IX and X cranial nerves, which then sends efferent signals to the muscles involved in swallowing, including the stylopharyngeus muscle. This reflex helps to assess the integrity of the nucleus ambiguus and the cranial nerves that innervate it.

**Why Each Wrong Option is Incorrect**
**Option A:** The corneal reflex tests the integrity of the trigeminal nerve (cranial nerve V) and the facial nerve (cranial nerve VII), not the nucleus ambiguus.
**Option B:** The jaw jerk reflex tests the integrity of the trigeminal nerve (cranial nerve V), not the nucleus ambiguus.
**Option C:** The oculovestibular reflex tests the integrity of the vestibulocochlear nerve (cranial nerve VIII), not the nucleus ambiguus.

**Clinical Pearl / High-Yield Fact**
The gag reflex is an important clinical sign that can indicate the presence of a lesion affecting the nucleus ambiguus or the cranial nerves IX and X. In patients with a gag reflex, a unilateral lesion affecting one of these nerves may result in a diminished or absent gag reflex on the same side.

**Correct Answer:** C.