  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 $\textit{complex time-reversible}$ 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 $\textit{kinematic}$ 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.
