A 64-year-old man is evaluated after an ischemic stroke. Over the last 24 hours, he has developed slurred speech and difficulty swallowing liquids with coughing. On exam, the uvula deviates to the left with phonation and the patient has a hoarse voice. He has no facial weakness. MRI shows an infarct involving the rostral medulla. Which brainstem nucleus is most directly responsible for this patient’s impaired swallowing and hoarseness?

(Assume the lesion affects the nucleus itself rather than peripheral nerve fibers.)