Turns out that ENSO is a straightforward tidal forcing. In 1776, Pierre-Simon Laplace came up with equations that later evolved into the more complex Navier-Stokes equations. However, for many fluid dynamics applications that don't have much viscosity, these so-called Laplace's Tidal Equations are adequate. And so as should be obvious, Laplace's Tidal Equations imply that tides provide the forcing. How can the entire climate science community not be able to solve these equations and apply them properly? Beats me.
One aspect that is tricky about the forcing is that the two major factors -- the tropical fortnightly (**Mf**=13.66d) and the anomalistic monthly (**Mm**=27.55d) are actually aliased quite closely in comparison to the annual impulse. The difference is so small that the repeat cycle for just these two factors is 180 years, which means the fitting process is painful on top of the non-linear iteration required. Yet it is amazing on how few degrees of freedom in the synchronous forcing is required to match to the empirical results and also to cross-validate against the out-of-band testing interval. See below. Detailed tidal analysis has always been about the combinatorics of the primary factor harmonics -- the tropical, draconic, anomalistic cycles interfering with the annual cycle. Then the 1/R^3 gravitational forcing will automatically create the 9-day (**Mt**) and 6-day (**Msq**) harmonics, and the solution to LTE will throw it all in to the grinder and one has to decode the non-linear harmonics generation via your choice of iteration. A gradient descent algorithm will work, as will a brute force random descent given enough time.
Unfortunately, climate scientists continue to be mystified by all this. Earth sciences is not a discipline that attracts the curious from what I have discovered.