Image differences between the eyes can cause millisecond-scale interocular differences in processing speed. For moving objects, these differences can cause dramatic misperceptions of distance and 3D direction. Here, we develop a continuous target-tracking paradigm for measuring these processing differences. Human observers continuously tracked a target stimulus with various luminance differences across the eyes as it underwent Brownian motion in the horizontal plane. We show that suitable analysis recovers the time course of the visuomotor response, and comparisons across conditions reveal the temporal evolution of visual processing differences between the eyes. Next, we show analytically, and partially confirm experimentally, that the interocular difference between the temporal impulse response functions predicts how lateral target motion impacts the motion-in-depth response. Finally, using a direct within-observer comparison, we show that target tracking and traditional psychophysics provide scalar estimates of interocular delays that agree on average to within a fraction of a millisecond. Thus, target tracking accurately recovers millisecond-scale differences in processing speed while revealing the millisecond-by-millisecond time course of visual processing, all in a fraction of the time required by traditional methods. This paradigm provides the potential for new predictive power, the application of analytical techniques from computational neuroscience, and the rapid measurement of clinical and developmental populations in which traditional psychophysics might be impractical.