Here is a hypothesis.

There was a known event called the Pacific climate shift of 1976-1977. What happens as a result of this climate shift is that the characteristic frequency $\omega_0$ started increasing from a value 1.5 rad/year to a value of 2.7 rad/year. This would cross the threshold at which the QBO oscillation shifted from one sign to another. There would be a significant resonance when this happened. And of course the EN of 1982-1983 was the biggest of the century up to that point.
http://www.whoi.edu/science/B/people/kamaral/1982-1983ElNino.html

Plus consider the fact that a significant volcano erupted in 1982 which may have also been the spark for a temporary characteristic frequency change, potentially due to changes in the density at the thermocline as less sunlight entered the water. This is a very narrow interval at which this all happened though so is somewhat questionable.

The disturbance eventually died out and then ended in 1996, right in time for another phase reversal for the huge 1998 EN event, which then locked in to the original phase alignment that was there before 1980.

Note the observation by Chao in comment #16, where he mentions the polarity changes with respect to QBO for the two events.

This is perhaps a bit too tidy but it makes an interesting narrative.

Excited yet?