**Core Concept**
The secretomotor fibers of the facial nerve (cranial nerve VII) are responsible for transmitting parasympathetic signals to various glands and muscles in the head and neck. These fibers originate from the superior salivatory nucleus and the inferior salivatory nucleus, and they play a crucial role in regulating the secretion of saliva, tear production, and other autonomic functions.

**Why the Correct Answer is Right**
The correct answer will be the structure that does not receive secretomotor innervation from the facial nerve. To determine this, let's examine the options and their respective innervations:
- **Option A:** The lacrimal gland is indeed supplied by secretomotor fibers of the facial nerve, which stimulate tear production.
- **Option B:** The submandibular gland receives secretomotor innervation from the facial nerve, which regulates saliva production.
- **Option C:** The sublingual gland also receives secretomotor innervation from the facial nerve, similar to the submandibular gland.
- **Option D:** The pharyngeal plexus, which supplies the pharyngeal muscles, is primarily innervated by the glossopharyngeal nerve (cranial nerve IX) and the vagus nerve (cranial nerve X), rather than the facial nerve.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because the lacrimal gland does receive secretomotor innervation from the facial nerve.
**Option B:** This option is incorrect because the submandibular gland does receive secretomotor innervation from the facial nerve.
**Option C:** This option is incorrect because the sublingual gland does receive secretomotor innervation from the facial nerve.

**Clinical Pearl / High-Yield Fact**
The facial nerve's secretomotor fibers play a vital role in maintaining the health and function of the lacrimal and salivary glands. This is why damage to the facial nerve, such as in Bell's palsy, can lead to dry eyes and mouth.

**Correct Answer:** D. The pharyngeal plexus is not supplied by secretomotor fibers of the facial nerve.