Hey DM! Yes, the Equinoxs are common start times for cycles. I think the Solstices come next. As for stats, you can just Google Clusters and see what pops. I am not aware of any.
Personally, I have had all but one cycle start in September and run till March - Spring to Fall Equinox. Then this year, I had a cycle start in late June. So, there ya go! This after decadees too.
Very possibly you will only have one cycle per year. So, just be prepared.
ATB!