In the last comment, I mentioned that the 5.643 and 3.447 year aliased tidal factors may contribute to the ENSO model fit. I needed to increase the interval width at the expense of overlapping the Low and High intervals. The reason for this is that 5.643 is relatively close to 6.41 and so the discrimination region needs to be wider.
This factor does markedly improve the overall fit, as you can see in both the Low and High fits how well the 2016 El Nino peak was captured.
Shown next are the correlations for the individual factors. The 5.643 period correlation Low vs High is at the bottom. The CC values are all ~0.8 or greater.
In contrast as shown next, the 3.447 period correlation Low vs High is not strong and the contribution to the fit is relatively weak
This does not imply the factor is not there, only that more work is needed to reveal it. The Mathieu modulation converges as well, but this is at least partly due to the overlapping interval fit: