The brighter water masers of NGC 1068 appear to trace molecular gas in a parsec-scale disk surrounding the central engine. We find evidence that these masers are reverberating in response to a central, common pump source, presumably the central engine. Firstly, the luminosities of individual maser features are correlated on time-scales as fine as years, even though the dynamical time is 10000 years. Secondly, we have detected a simultaneous flare event among blueshifted masers and redshifted masers; the flare signal is symmetric in Doppler velocity about the systemic velocity of the galaxy. Thirdly, we present a model in which a 1988 X-ray flare of the central engine may have caused (1) the loss of maser signal over the period 1990--1991, and (2) a subsequent peak of emission from warm dust between 1994 and 1995. Although the present data are not sufficient to pin down an accurate, geometric distance measure, they favor a distance of 18 Mpc to NGC 1068. We demonstrate how further monitoring may provide a more accurate distance measurement.