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While secondary mass inferences based on single-lined spectroscopic binary (SB1) solutions are subject to$\sin i$degeneracies, this degeneracy can be lifted through the observations of eclipses. We combine the subset of Gaia Data Release 3 SB1 solutions consistent with brown dwarf-mass secondaries with the Transiting Exoplanet Survey Satellite (TESS) Object of Interest (TOI) list to identify three candidate transiting brown dwarf systems. Ground-based precision radial velocity follow-up observations confirm that TOI-2533.01 is a transiting brown dwarf with$M={72}_{-3}^{+3}{M}_{\mathrm{Jup}}={0.069}_{-0.003}^{+0.003}{M}_{\odot }$orbiting TYC 2010-124-1 and that TOI-5427.01 is a transiting very low-mass star with$M={93}_{-2}^{+2}{M}_{\mathrm{Jup}}={0.088}_{-0.002}^{+0.002}{M}_{\odot }$orbiting UCAC4 515-012898. We validate TOI-1712.01 as a very low-mass star with$M={82}_{-7}^{+7}{M}_{\mathrm{Jup}}={0.079}_{-0.007}^{+0.007}{M}_{\odot }$transiting the primary in the hierarchical triple system BD+45 1593. Even after accounting for third light, TOI-1712.01 has a radius nearly a factor of 2 larger than predicted for isolated stars with similar properties. We propose that the intense instellation experienced by TOI-1712.01 diminishes the temperature gradient near its surface, suppresses convection, and leads to its inflated radius. Our analyses verify Gaia DR3 SB1 solutions in the low Doppler semiamplitude limit, thereby providing the foundation for future joint analyses of Gaia radial velocities and Kepler, K2, TESS, and PLAnetary Transits and Oscillations light curves for the characterization of transiting massive brown dwarfs and very low-mass stars.