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The majority of brown dwarfs show some level of photometric or spectro-photometric variability in different wavelength ranges. This variability allow us to trace the 3D atmospheric structures of variable brown dwarfs and directly-imaged exoplanets with radiative-transfer models and mapping codes. Nevertheless, to date, we do not have an informed method to pre-select the brown dwarfs that might show a higher variability amplitude for a thorough variability study. In this work, we designed and tested near-infrared spectral indices to pre-select the most likely variable mid- and late-T dwarfs, which overlap in effective temperatures with directly-imaged exoplanets. We used time-resolved near-infrared Hubble Space Telescope Wide Field Camera 3 spectra of a T6.5 dwarf, 2MASS J22282889--431026, to design our novel spectral indices. We tested these spectral indices on 26 T5.5--T7.5 near-infrared SpeX/IRTF spectra, and we provided eight new mid- and late-T variable candidates. We estimated the variability fraction of our sample in $38^{+4}_{-30}$%, which agrees with the variability fractions provided by Metchev, et. al, (2015) for mid-to late-T dwarfs. In addition, two of the three previously known variables in our SpeX spectra sample are flagged as variable candidates by our indices. Similarly, all seven known non-variable in our sample are flagged as non-variable objects by our indices. These results suggest that our spectral indices might be used to find variable mid- and late-T brown dwarf variables. These indices may be crucial in the future to select cool directly-imaged exoplanets for variability studies.