Hot subdwarf stars are mostly stripped red giants that can exhibit photometric variations due to stellar pulsations, eclipses, the reflection effect, ellipsoidal modulation, and Doppler beaming. Detailed studies of their light curves help constrain stellar parameters through asteroseismological analyses or binary light-curve modeling and generally improve our capacity to draw a statistically meaningful picture of this enigmatic stage of stellar evolution. From an analysis of Gaia DR2 flux errors, we have identified around 1200 candidate hot subdwarfs with inflated flux errors for their magnitudes-a strong indicator of photometric variability. As a pilot study, we obtained 2 minute cadence TESS Cycle 2 observations of 187 candidate hot subdwarfs with anomalous Gaia flux errors. More than 90% of our targets show significant photometric variations in their TESS light curves. Many of the new systems found are cataclysmic variables, but we report the discovery of several new variable hot subdwarfs, including HW Vir binaries, reflection-effect systems, pulsating sdBVs stars, and ellipsoidally modulated systems. We determine atmospheric parameters for select systems using follow-up spectroscopy from the 3m Shane telescope. Finally, we present a Fourier diagnostic plot for classifying binary light curves using the relative amplitudes and phases of their fundamental and harmonic signals in their periodograms. This plot makes it possible to identify certain types of variables efficiently, without directly investigating their light curves, and may assist in the rapid classification of systems observed in large photometric surveys.