Final answer:
The back of the tongue is most likely to trigger the gag reflex. The glossopharyngeal nerve and vagus nerve control this reflex.
Step-by-step explanation:
The area most likely to trigger the gag reflex is the back of the tongue.
When the tongue depressor is moved to contact the lateral wall of the fauces, it typically elicits the gag reflex.
This reflex is mediated by the glossopharyngeal nerve and the motor response is controlled by the vagus nerve.