There is no cross-talk. There is only a common-mode forcing.
ENSO and AMO have essentially no time-series cross-correlation.
$$ ENSO = g (f(t)) $$
$$ AMO = h (f(t)) $$
*f(t)* is the tidal forcing and it is virtually the same for the Pacific and Atlantic oceans. The only factor that differs is the basin geometry that sets the Laplace's Tidal Equation standing-wave modes, which are correspondingly described by a small set of sinusoidal modulation terms -- a couple for *g(x)* and a couple for *h(x)*.
**There is no possible way that a chance selection of these terms can generate a SIMULTANEOUS match to ENSO and AMO**
It's hard enough to fit to one model at a time. But once you estimate *x=f(t)* and then iterate on *g(x)* for ENSO, then the *h(x)* for AMO is straightforward to extract since *f(t)* is essentially fixed.
The climate scientist Michael Mann published a Science article this month whereby his research team claims that AMO isn't even an oscillation -- [Multidecadal climate oscillations during the past millennium driven by volcanic forcing](https://science.sciencemag.org/content/371/6533/1014)
> "The Atlantic Multidecadal Oscillation (AMO), a 50- to 70-year quasiperiodic variation of climate centered in the North Atlantic region, was long thought to be an internal oscillation of the climate system. Mann et al. now show that this variation is forced externally by episodes of high-amplitude explosive volcanism."