The re-emergence of the 0.99 \mu m FeH feature in brown dwarfs of early- to mid-T spectral type has been suggested as evidence for cloud disruption where flux from deep , hot regions below the Fe cloud deck can emerge . The same mechanism could account for color changes at the L/T transition and photometric variability . We present the first observations of spectroscopic variability of brown dwarfs covering the 0.99 \mu m FeH feature . We observed the spatially resolved very nearby brown dwarf binary WISE J104915.57-531906.1 ( Luhman 16AB ) , a late-L and early-T dwarf , with HST/WFC3 in the G102 grism at 0.8-1.15 \mu m. We find significant variability at all wavelengths for both brown dwarfs , with peak-to-valley amplitudes of 9.3 % for Luhman 16B and 4.5 % for Luhman 16A . This represents the first unambiguous detection of variability in Luhman 16A . We estimate a rotational period between 4.5 and 5.5 h , very similar to Luhman 16B . Variability in both components complicates the interpretation of spatially unresolved observations . The probability for finding large amplitude variability in any two brown dwarfs is less than 10 % . Our finding may suggest that a common but yet unknown feature of the binary is important for the occurrence of variability . For both objects , the amplitude is nearly constant at all wavelengths except in the deep K I feature below 0.84 \mu m. No variations are seen across the 0.99 \mu m FeH feature . The observations lend strong further support to cloud height variations rather than holes in the silicate clouds , but can not fully rule out holes in the iron clouds . We re-evaluate the diagnostic potential of the FeH feature as a tracer of cloud patchiness .