We demonstrate that the 'smoke' of limited instrumental sensitivity smears out structure in gamma-ray burst (GRB) pulse light curves, giving each a triple-peaked appearance at moderate signal-to-noise and a simple monotonic appearance at low signal-to-noise. We minimize this effect by studying six very bright GRB pulses (signal-to-noise generally > 100), discovering surprisingly that each exhibits complex time-reversible wavelike residual structures. These 'mirrored' wavelike structures can have large amplitudes, occur on short timescales, begin/end long before/after the onset of the monotonic pulse component, and have pulse spectra that generally evolve hard to soft, re-hardening at the time of each structural peak. Among other insights, these observations help explain the existence of negative pulse spectral lags, and allow us to conclude that GRB pulses are less common, more complex, and have longer durations than previously thought. Because structured emission mechanisms that can operate forwards and backwards in time seem unlikely, we look to kinematic behaviors to explain the time-reversed light curve structures. We conclude that each GRB pulse involves a single impactor interacting with an independent medium. Either the material is distributed in a bilaterally symmetric fashion, the impactor is structured in a bilaterally symmetric fashion, or the impactor's motion is reversed such that it returns along its original path of motion. The wavelike structure of the time-reversible component suggests that radiation is being both produced and absorbed/deflected dramatically, repeatedly, and abruptly from the monotonic component.