PaulP: "Nothing has been known to disturb the cycles of ENSO"
So I pointed out ENSO cycles are known inherently disturbed, which is as you say, the "Problem Statement" (not punting).
In fact, many things can throw ENSO. Plate tectonics are heuristically guaranteed to "disturb (create-change-destroy) cycles of ENSO", and many other probable events must be able to throw ENSO, like Ice-Age/SnowBall-Earth phases, major Asteroid Strikes, or Anthropogenic Climate Change.
The photo of TIW in fact shows Doppler wavelength variation (see right side). TIW is an apparent non-lunisolar Helmholz resonance. The equatorial wave guide is not perfect. Its subject to seasonal kicks like the ITCZ itself is. Its far from a perfect Topological Insulator either. Speaking of which, the sea surface and internal thermocline are Anyonic channels, further hyper-complicating the hyper-chaotic picture. "Noise" is simply what we call deterministic chaos before we sort out the details.
Geophysical sensor networks are made of small cells subject to lots of local noise, even if the bulk event is relatively immune to local noise, as you claim. Bulk events are hard to pinpoint in spacetime, and in principle embody micro-chaos around an idealized center and relativistic time-base very hard to actually observe.
In the 60Hz analogy, just as you argue, "the spatial pattern is easily predicted", but if overlaid on Beethoven, it does not follow that its forcing the music signal. Ideally you want to prove lunisolar forcing, not just leave open that tidal signals may be corrupting ENSO data. If you still doubt there is any proof possible in mathematical physics, that may stop you from persevering.
Here is NASA studying Jupiter's QQO version of Earth's QBO. Obviously, Jupiter's oscillation is not forced by huge lunisolar tides:
Jupiter's year is 11.86 Earth years, its day is 9hr 55min, and its moons are tiny by comparison.