This clinical study evaluates over medium-to-long term the hypothesis that intermittent spontaneous ocular choroidal vasculature-related congestive and nociceptive corneoscleral envelope distention have a pathogenetic role in genesis of episodic lateralizing migraine headache attacks. No neuro-anatomic or -physiologic difference prevails between the three divisions of the trigeminal nerve, but migraine dominantly affect the ophthalmic division. Use of topical ophthalmic solution for managing acute headache attacks of migraine has given contradictory results in controlled trials. I report the distribution of weekend-migraine headache attacks on a single‐participant (N=1) level for 2 patients over a 3-year period (2017-2020) without misuse of any recreational drug other than caffeine on week-days. After a run-in basal period of 6-months recorded on their Smartphones app, with their informed consent, a trial was carried out with topical long-acting β-blocker timolol maleate 0.5% w/v ophthalmic solution once weekly on Saturday night just before sleeping with no other advice to promote nocturnal sleeping or early awakening the next morning; only alcohol binge was proscribed. No week-end attacks of lateralizing migraine headache were reported in the 2 patients over a period of 3- years, a long-term consistent response. The biologically-plausible and defensible mechanistic link between migraine, intraocular pressure, ocular choroidal vasculature, nociceptive corneoscleral envelope aberration, and the pharmacologic basis for therapeutic ocular hypotension for prophylaxis of migraine headache attacks is elucidated for the first time in migraine literature.