Final answer:
The submandibular and sublingual glands receive parasympathetic stimulation from the facial nerve that synapses in the submandibular ganglion, while sympathetic modulation comes from the superior cervical ganglion.
Step-by-step explanation:
The neural control of the submandibular gland and the sublingual gland arises from the parasympathetic fibers of the facial nerve, specifically the chorda tympani branch, which synapses in the submandibular ganglion. From here, postganglionic fibers project to stimulate the submandibular glands and sublingual glands, promoting salivation. Conversely, the sympathetic innervation that modulates the function of these glands originates from the superior cervical ganglion, which projects postganglionic fibers to the glands, usually resulting in a reduction in saliva secretion.