We report the detection of radio emission and orbital motion from the nearby star-brown dwarf binary WISE J072003.20-084651.2AB. Radio observations across the 4.5-6.5 GHz band with the Very Large Array identify at the position of the system quiescent emission with a flux density of 15$pm$3 $mu$Jy, and a highly-polarized radio source that underwent a 2-3 min burst with peak flux density 300$pm$90 $mu$Jy. The latter emission is likely a low-level magnetic flare similar to optical flares previously observed for this source. No outbursts were detected in separate narrow-band H$alpha$ monitoring observations. We report new high-resolution imaging and spectroscopic observations that confirm the presence of a co-moving T5.5 secondary and provide the first indications of three-dimensional orbital motion. We used these data to revise our estimates for the orbital period (4.1$^{+2.7}_{-1.3}$ yr) and tightly constrain the orbital inclination to be nearly edge-on (93.6deg$^{+1.6deg}_{-1.4deg}$), although robust measures of the component and system masses will require further monitoring. The inferred orbital motion does not change the high likelihood that this radio-emitting very low-mass binary made a close pass to the Sun in the past 100 kyr.