Which headache type is often precipitated by alcohol ingestion and characterized by severe periorbital pain?

Cluster headaches are a primary headache disorder known for their distinctive characteristics, including severe, unilateral periorbital (around the eye) pain that can be exquisitely painful. These headaches often occur in groups or "clusters" over a period of time, followed by remission periods. A notable feature of cluster headaches is their tendency to be triggered by specific factors, with alcohol ingestion being one of the most common triggers during a cluster period.

In contrast, tension headaches typically present as a band-like tightness or pressure around the head and are not usually associated with periorbital pain or alcohol as a precipitating factor. Migraines can present with unilateral pain and may have triggers including alcohol, but the pain is more varied in location and can occur with additional neurological symptoms like aura or photophobia. Cervicogenic headaches stem from cervical spine issues and do not typically cause the severe, localized periorbital pain associated with cluster headaches.

Thus, the strong association between alcohol consumption and the onset of intense, localized headaches around the eye region distinctly supports cluster headaches as the correct answer.