  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 (DR) 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 $M=72^{+3}_{-3}~M_{\text{Jup}}=
0.069^{+0.003}_{-0.003}~M_\odot$ orbiting TYC 2010-124-1 and that TOI-5427.01
is a transiting very low-mass star with
$M=93^{+2}_{-2}~M_{\text{Jup}}=0.088^{+0.002}_{-0.002}~M_\odot$ orbiting UCAC4
515-012898. We validate TOI-1712.01 as a very low-mass star with
$M=82^{+7}_{-7}~M_{\text{Jup}}=0.079^{+0.007}_{-0.007}~M_\odot$ transiting the
primary in the hierarchical triple system BD+45 1593. Even after accounting for
third light, TOI-1712.01 has radius nearly a factor of two 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 (PLATO) light curves for the characterization of transiting
massive brown dwarfs and very low-mass stars.
