PaulP: "any time scale we would be interested in"
All time scales are scientifically interesting. You objected to lack of curiosity recently, only to now profess your own disinterest (?) ENSO was set up by plate tectonics and many other long period factors. Chaos occurs at all scales.
PaulP: "bad science that NOAA perpetrated by removing the annual signal from the ENSO time-series."
What reference for this bad science? NOAA has thousands of scientists and many models. NOAA can't be all "bad science" and "laughable ignorance" anymore than if you were unfairly dissed so.
PaulP: "ENSO is not chaotic, but rather non-linear deterministic"
ENSO is both; deterministic chaos is non-linear. You have your work cut out proving ENSO is not chaotic without knowing chaos science in depth.
You continue to ignore the need to quantify and filter-out real-time Lunisolar tidal noise in ENSO sensor array data. That's good science to "catch up at some point"; to accurately resolve ENSO Lunisolar Forcing versus ENSO Chaos.
Lets take a close look at NOAA's buoy networks, and the tidal noise they are subject to. Here is a start-
Lets consider at your latest factor of interest- horizontal pull of Lunar Tide; specifically on an ENSO data-collection sea-buoy anchored several kilometers deep. Regardless of what wind and current otherwise does, the buoy will experience a definite tidal yanking captured by the multi-sensor data streams. This superposed yanking sequence will indeed encode Lunisolar cycle complexities. Here is part of the appearance in data of ENSO Tidal forcing and noise, but how much of which? I guess its mostly noise, but nobody knows for sure.
Thanks for your patience addressing the loose ends.