**Core Concept**
The question requires identification of structures passing between the base of the skull and the superior constrictor muscle. The superior constrictor muscle is one of the three pharyngeal constrictors and is located in the pharyngeal wall. The base of the skull and the superior constrictor muscle form a boundary that divides the pharynx into different compartments.

**Why the Correct Answer is Right**
The glossopharyngeal nerve (cranial nerve IX) is primarily responsible for swallowing and taste sensation in the posterior one-third of the tongue. However, it does not pass between the base of the skull and the superior constrictor muscle. Instead, it passes through the jugular foramen, which is located at the base of the skull, but outside the pharyngeal wall. This is in contrast to the other options, which are all structures that pass between the base of the skull and the superior constrictor muscle.

**Why Each Wrong Option is Incorrect**
**Option B:** Pharyngobasilar fascia is a layer of connective tissue that covers the pharyngeal muscles, including the superior constrictor, and separates them from the base of the skull. It does indeed pass between the base of the skull and the superior constrictor muscle.
**Option C:** The Eustachian tube (or auditory tube) connects the middle ear to the nasopharynx and passes through the base of the skull, between the superior constrictor muscle and the base of the skull.
**Option D:** The levator veli palati muscle is one of the muscles of the soft palate and passes between the base of the skull and the superior constrictor muscle.

**Clinical Pearl / High-Yield Fact**
When identifying structures passing between the base of the skull and the superior constrictor muscle, it's essential to remember that the pharyngobasilar fascia, Eustachian tube, and levator veli palati muscle are all part of this group. This knowledge is crucial for understanding the anatomy of the pharynx and the base of the skull.

**✓ Correct Answer: A. Glossopharyngeal nerve**