Sloshing of the ocean's waters, as exemplified by ENSO, can only be generated by a suitable forcing. Nothing will spontaneously slosh back and forth unless it gets the right excitation. Some might hold a naive picture that simply the rotation of the earth can cause the sloshing, but we have to remember that this is a centrifugal force which is evenly directed downward with no changes over time. However, this last part -- "no changes over time" -- is only correct to zero-th order. Two classes of mechanisms can disrupt this constant rotation rate. First, the Chandler wobble of the earth's axis causes a continuously changing angular momentum of a point of reference. That is a general wobble mechanism similar to the spinning of a top. The second class is of nonspecific events that can either speed up or slow down the rotation rate of the earth. Note that the wobble may be a behavior that actually belongs to this class, as it may be hard to distinguish the specific mechanisms behind the change in rate. Both of these mechanisms have been measured and they both indicate a clear periodic signal of approximately 6 years. The Chandler wobble was described in a previous SOI modeling post and it shows a strong average period of 6.45 years see Figure 1 below.
Holme and Viron  measured the second mechanism by sensitive characterization of the length of day (LOD) data. They only go back to 1964, but find a clear 5.9 year period in the LOD variations (see Figure 2 below). The LOD delta is inversely related to an angular momentum change.
The jumps are well known in the Chandler Wobble literature and show up on the standard plot of X vs Y polar motion as transient poleward slips, see the yellow region in Figure 5 below. Ongoing research  characterizes these as jerks, which is a higher order acceleration term.
It is entirely possible that these transients are responsible for changing the angular momentum from a 6.45 year period to the 5.9 year period shown in the LOD data. Observing 10 significant slips/jerks over the span of 100 years, indicates that a 10% change in period may occur as well. Note that I haven't worked out a good model for this and am simply going on intuition to what may be happening.
Update: A May paper describes possible associations between the lunar nodal cycle, Chandler wobble, and Arctic climate:
H. Yndestad, “The influence of the lunar nodal cycle on Arctic climate,” ICES Journal of Marine Science: Journal du Conseil, vol. 63, no. 3, pp. 401–420, Jan. 2006.
"Why are the lunar cycles so dominant? The polar movement is only 3–15 m, and the lunar nodal tide represents only a small fraction of daily sea-level changes, so why are there dominant lunar nodal cycles in the time-series? The answer lies in the fundamental difference between stationary and random cycles. Small changes in stationary cycles have great influence when they are integrated in time and space. Hence there would not be a fixed signal-to-noise ratio: the ratio, it would increase over time and space."
 R. Holme and O. de Viron, “Characterization and implications of intradecadal variations in length of day,” Nature, vol. 499, no. 7457, pp. 202–204, 2013. PDF
 A. Chulliat and S. Maus, “Geomagnetic secular acceleration, jerks, and a localized standing wave at the core surface from 2000 to 2010,” J. Geophys. Res. Solid Earth, vol. 119, no. 3, pp. 1531–1543, Mar. 2014.
 E. Bellanger, D. Gibert, and J.-L. Le Mouël, “A geomagnetic triggering of Chandler wobble phase jumps?,” Geophys. Res. Lett., vol. 29, no. 7, pp. 28–1, Apr. 2002.