Dryness of eye is caused by injury to facial nerve at:
(d) Geniculate ganglion(Ref. Cummings, 6th ed., 2606)Whenever there is injury before or at the origin of the greater superficial petrosal nerve (i.e. before or at the Geniculate ganglion) which is responsible for lacrimation there will be dry eye on the same side.Tympanic segment, Vertical segment and Chorda tympani all are beyond the geniculate ganglion.
Chorda tympani
Vertical segment
Tympanic segment
Geniculate ganglion
Facial Nerve And Its Disorders