**Core Concept**
Facial nerve palsy can occur due to various causes, including lesions at different points along its course from the brainstem to the stylomastoid foramen. The stylomastoid foramen is a critical location where the facial nerve exits the skull and enters the parotid gland. A lesion at this site can cause weakness or paralysis of the facial muscles.

**Why the Correct Answer is Right**
The test that can detect facial nerve palsy occurring due to a lesion at the outlet of the stylomastoid foramen is the **Stapedius reflex test**. This reflex involves the contraction of the stapedius muscle, which is innervated by the facial nerve, in response to a loud sound. The stapedius reflex is preserved in cases of upper motor neuron lesions but is abolished in cases of lower motor neuron lesions, including those at the stylomastoid foramen. This makes the stapedius reflex test a useful tool for detecting facial nerve palsy at this specific location.

**Why Each Wrong Option is Incorrect**
* **Option A:** The corneal reflex test detects facial nerve palsy at the level of the geniculate ganglion, not the stylomastoid foramen.
* **Option B:** The taste test detects facial nerve palsy at the level of the chorda tympani, not the stylomastoid foramen.
* **Option D:** The blink reflex test detects facial nerve palsy at the level of the upper motor neurons, not the stylomastoid foramen.

**Clinical Pearl / High-Yield Fact**
The stapedius reflex test is a useful clinical tool for detecting facial nerve palsy, especially at the stylomastoid foramen. It is a simple and non-invasive test that can be performed in a clinical setting.

**Correct Answer:** C.