We report new (1995) Very Large Array (VLA) observations and (1984-1999) Effelsberg 100 m monitoring observations of the 22 GHz H2O maser spectrum of the Seyfert 2 galaxy NGC 1068. The sensitive VLA observations provide a registration of the 22 GHz continuum emission and the location of the maser spots with an accuracy of ~5 mas. Within the monitoring data, we find evidence that the nuclear masers vary coherently on timescales of months to years, much more rapidly than the dynamical timescale. We argue that the nuclear masers are responding in reverberation to a central power source, presumably the central engine. Between 1997 October and November, we detected a simultaneous flare of the blueshifted and redshifted satellite maser lines. Reverberation in a rotating disk naturally explains the simultaneous flaring. There is also evidence that near-IR emission from dust grains associated with the maser disk also responds to the central engine. We present a model in which an X-ray flare results in both the loss of maser signal in 1990 and the peak of the near-IR light curve in 1994. In support of rotating disk geometry for the nuclear masers, we find no evidence for centripetal accelerations of the redshifted nuclear masers; the limits are +/-0.006 km s-1 yr-1, implying that the masers are located within 2° of the kinematic line of nodes. We also searched for high-velocity maser emission like that observed in NGC 4258. In both VLA and Effelsberg spectra, we detect no high-velocity lines between approximately +/-350 and +/-850 km s-1 relative to systemic, arguing that masers only lie outside a radius of ~0.6 pc (1.9 lt-yr) from the central engine (assuming a distance of 14.4 Mpc). We also consider possible models for the jet masers near radio continuum component C. We favor a shock precursor model, in which the molecular gas surrounding the jet is heated by X-ray emission from a shock front between the jet and a molecular cloud.