  We use the Wide Field Camera 3 on the {\sl Hubble Space Telescope} to
spectrophotometrically monitor the young L7.5 companion HD~203030B. Our time
series reveal photometric variability at 1.27\,$\mu$m and 1.39\,$\mu$m on time
scales compatible with rotation. We find a rotation period of
$7.5^{+0.6}_{-0.5}$ h: comparable to those observed in other brown dwarfs and
planetary-mass companions younger than 300 Myr. We measure variability
amplitudes of $1.1\pm0.3\%$ (1.27\,$\mu$m) and $1.7\pm0.4\%$ (1.39\,$\mu$m),
and a phase lag of 56$^\circ\pm$28$^\circ$ between the two light curves. We
attribute the difference in photometric amplitudes and phases to a patchy cloud
layer that is sinking below the level where water vapor becomes opaque. HD
203030B and the few other known variable young late-L dwarfs are unlike warmer
(earlier-type and/or older) L dwarfs, for which variability is much less
wavelength-dependent across the 1.1--1.7$\mu$m region. We further suggest that
a sinking of the top-most cloud deck below the level where water or carbon
monoxide gas become opaque may also explain the often enhanced variability
amplitudes of even earlier-type low-gravity L dwarfs. Because these condensate
and gas opacity levels are already well-differentiated in T dwarfs, we do not
expect the same variability amplitude enhancement in young vs.\ old T dwarfs.
