## Core Concept
Harvard's criteria, also known as the "Harvard criteria for brain death," are a set of guidelines used to determine brain death in patients. These criteria involve the assessment of both clinical examination and ancillary tests. The clinical examination includes evaluation of brainstem reflexes.

## Why the Correct Answer is Right
The correct answer involves understanding which reflex is not part of Harvard's criteria for determining brain death. The reflexes typically tested include pupillary, corneal, oculovestibular (also known as caloric reflex), gag, and cough reflexes.

## Why Each Wrong Option is Incorrect
To accurately address this question, let's consider common reflexes tested:
- **Option A:** Pupillary reflex. This is tested as part of the brainstem reflex assessment, where the absence of pupillary reaction to light is one criterion.
- **Option B:** Corneal reflex. This reflex is also tested; its absence supports the diagnosis of brain death.
- **Option C:** Oculovestibular reflex (caloric reflex). This is another reflex tested; it assesses the integrity of the brainstem.
- **Option D:** Gag reflex. While historically considered, the gag reflex is not universally required for the diagnosis of brain death according to strict Harvard criteria but might be confused with cough reflex.

## Clinical Pearl / High-Yield Fact
A key point to remember is that while several reflexes are tested, not all are strictly necessary for the diagnosis. For instance, the absence of brainstem reflexes, including pupillary, corneal, and oculovestibular reflexes, is critical. The gag and cough reflexes are often tested but are not always included in strict criteria.

## Correct Answer Line
**Correct Answer: D. Gag reflex**