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 $1.1pm0.3%$ (1.27,$mu$m) and $1.7pm0.4%$ (1.39,$mu$m), and a phase lag of 56$^circpm$28$^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.
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