During the ear examination, cough occurs due to stimulation of
Arnold nerve. It is an auricular branch of jugular ganglion of the vagus. 
It supplies the skin of posterior part of pinna on the medial surface of the concha, and posterior wall of the external auditory canal and tympanic membrane.
The auricular nerve is the afferent limb of the Ear-Cough or Arnold Reflex.
Hypoglossal
Trochlear
Trigeminal
Vagus