One thing to notice on the phase reversals in #24 is that they occur near the origin. Recall the Mathieu differential equation for sloshing:
$ f''(t)+[a-2q\cos(2\omega t)]f(t)=F(t) $
where $F(t)$ is $ A sin(\pi t ) + B sin(2\pi t) + C sin(4\pi t ) $ ignoring all the phase constants for illustrative purposes
As $f(t)$ crosses zero, $f''(t)$ also nears an inflection point of zero if the waveform is near sinusoidal and has a zero mean value. This means that the forcing RHS, $F(t)$, has a greater influence on the direction that the waveform will take as it crosses the axis.
The premise is that the biennial forcing factor, $ A sin(\pi t ) $, has to be metastable to begin with since the earth favors neither odd years nor even years. And so the question becomes -- is this zero-crossing the point where the biennial oscillation could change from odd/even pairing in years to even/odd (or vice versa) ? And if there is a bias in the metastability, that it could change back on the next cycle, because one pairing is slightly favored ?