Glenn Brier is on my list of essential climate science researchers. I am sure he has since retired but his status as both a fellow of the American Meteorological Society and a fellow of the American Statistical Association indicated he knew his stuff. One of his research topics was exploring periodicities in climate data. He was eminently qualified for this kind of analysis as his statistics background provided him with the knowledge and skill in being able to distinguish between stochastic versus deterministic behaviors.
One paper Brier co-authored in 1989 is an obscure gem in terms of understanding the determinism of El Nino and ENSO . He essentially analyzed a 463-year historical chronology of strong El Nino events and was able to find significant periodicities of 6.75 and 14 years in the data.
This compares very well with what I have been able to decipher as the strongest ENSO periodicities (taken from the instrumental record since 1880) of 6.5 and 14 years.