Relation between trigeminal and facial nerve in sympathetic response
Certain parts of the facial nerve cooperatively share structure of trigeminal nerve. For example, to reach the sublingual gland, the chorda tympani of the facial nerve joins the mandibular branch of the lingual nerve. Additionally, to reach the lacrimal gland of the eye, the greater petrosal nerve branch of the facial nerve joins the structure of the maximallary branch of the trigeminal nerve.

For a pictorial demonstration of this, please refer to page 1069 of Clinically Oriented Anatomy 7th edition by Moore.