Esomeprazole, a proton pump inhibitor (PPI), is not a primary treatment for Cluster Headache but may be used adjunctively to manage potential gastric side effects of other medications. While its primary mechanism involves inhibiting gastric acid secretion by blocking the H+/K+ ATPase enzyme in gastric parietal cells, its role in Cluster Headache management is primarily supportive rather than direct symptomatic relief.