[abbreviated] We report resolved near-infrared spectroscopic monitoring of the nearby L dwarf/T dwarf binary WISE J104915.57-531906.1AB (Luhman 16AB), as part of a broader campaign to characterize the spectral energy distribution and temporal variability of this system. A continuous 45-minute sequence of low-resolution IRTF/SpeX data spanning 0.8-2.4 micron were obtained, concurrent with combined-light optical photometry with ESO/TRAPPIST. Our spectral observations confirm the flux reversal of this binary, and we detect a wavelength-dependent decline in the relative spectral fluxes of the two components coincident with a decline in the combined-light optical brightness of the system over the course of the observation. These data are successfully modeled as a combination of brightness and color variability in the T0.5 Luhman 16B, consistent cloud variations; and no significant variability in L7.5 Luhman 16A. We estimate a peak-to-peak amplitude of 13.5% at 1.25 micron over the full lightcurve. Using a two-spot brightness temperature model, we infer an average cloud covering fraction of ~30-55% for Luhman 16B, varying by 15-30% over a rotation period. A Rhines scale interpretation for the size of the variable features explains an apparent correlation between period and amplitude for three highly variable T dwarfs, and predicts relatively fast winds (1-3 km/s) for Luhman 16B consistent with lightcurve evolution on an advective time scale (1-3 rotation periods). Our observations support the model of a patchy disruption of the mineral cloud layer as a universal feature of the L dwarf/T dwarf transition.
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