I'm a believer 100%
I think BP affects the HP gland and the sinuses both so you get it as a primary cause to start a cycle and a secondary cause to continue with cluster headaches. I personally think BP is the main driver over all of it... Seasonal BP changes, daily BP changes, coastal BP changes, weather BP changes.
I think our HP picks up on it ever so sensitive.. Ch sufferers have a genetic defect in out HP gland that makes us too sensitive to the change and we over react. This would explain chronic and episodic.
Any other infection in sinuses via allergy, cold or air plane, is a compounding affect with natural BP changes and this amplifies into enough to confuse the HP to trip and bam your next cycle starts.