One of the reasons that the metastable biennial nature of ENSO is not particularly foreign to me is that I recall grappling with a similar issue during my grad school days.
We were trying to grow GaAs layers on Ge for the long-term objective of optoelectronic integration -- optical column III-V compounds on electronic column IV substrates. I have the paper here on my ResearchGate site:
[Suppression of antiphase domains in the growth of GaAs on Ge(100) by molecular beam epitaxy](https://www.researchgate.net/publication/222779719_Suppression_of_antiphase_domains_in_the_growth_of_GaAs_on_Ge100_by_molecular_beam_epitaxy), Journal of Crystal Growth 81(1):214-220 · February 1987
If you read this you will see how we were able to infer that the Ge surface flipped from a natural 2-atomic-step pattern to a double 4-atomic step pattern when elemental As was applied.
Now, consider that this situation is completely metastable because the initiation of period doubling could occur on even-numbered step sequences or on odd-numbered sequences (with the sequence starting from some arbitrary point on the surface). That's the *spatial* equivalent of ENSO potentially adopting a biennial period in the time domain.
Yet, because we had laboratory control over the environment, we were able to watch when this metastable transition became completely mixed with anti-phase domains, which are mixtures of even and odd-sequenced steps. (you can see from all the experimental data that I used to be quite the lab rat at one time)
The problem is that -- with climate data -- we have absolutely no experimental controls we can place on anything, so all we can do is infer. So this coherent metastable doubling phenomenon does occur in nature, but how to validate the effect is where it gets tricky.