This is a magnification of the fitting contour around the best forcing period values for ENSO. These pair of peak values are each found to be less than a minute apart from the known values of the Draconic cycle (27.2122 days) and Anomalistic cycle (27.5545 days).
The forcing comes directly from the angular momentum variations in the Earth's rotation. The comparison between what the ENSO model uses (from the Draconic and Anomalistic terms above) and what is measured via monitoring the length-of-day (LOD) is shown below
The lower LOD pane is a fit over 3 years, which is about 40 lunar months. These essentially get aliased in the upper ENSO pane, which only responds to the peak tidal forces at a specific time of the year -- around Nov/Dec.
So many numbers have to align perfectly for this model to work out, and it looks like it does.