I did some searching and could again find very little on why the low-pass-filtered sea-level height anomaly (SLHA) shows an obvious exact 2-year periodic variation over spans of 50 years. It is not the quasi-biennial period of 2.33 years that ENSO shows.
This is analysis from a year ago for Sydney Harbor tide data:
But if the 2-year period is removed from SLHA via a crude notch filter, then the agreement with ENSO SOI is evident
There are likely two modes in the SLHA, a biennial mode and an ENSO mode.
This is close to the problem described:
Kim, Kwang-Yul, James J. O'Brien, and Albert I. Barcilon. "The principal physical modes of variability over the tropical Pacific." Earth Interactions 7.3 (2003): 1-32.
I will add this SLHA data to the entroplet server so I can let the MLR algorithm try to sort it out.