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I think this is a possible direction to go, based on some very promising results that I worked on over the past day.
For all I know, this may be a well known correlation, but I discovered that the tidal gauge data in Sydney Harbor aligns with the SOI behavior remarkably well, especially if a delay differencing of about 2 years is applied.
The tidal data itself has a significant annual and bi-annual periodicity modulated by an erratic envelope, potentially modeled by a DiffEq as shown below.
Another interesting teleconnection to consider !