Step 1: A reliable shortcut links every pharyngeal arch muscle to the cranial nerve that follows it.
Step 2: The glossopharyngeal nerve is the nerve of the third arch. Because the stylopharyngeus is the muscle supplied by the glossopharyngeal nerve, it must be the third arch muscle.
Step 3: By contrast, tensor tympani belongs to arch one (trigeminal mandibular supply), and cricothyroid belongs to arch four (vagus, external laryngeal nerve), so both are excluded.
Step 4: The single third arch derivative is therefore confirmed.
\[\boxed{\text{Stylopharyngeus}}\]