  NASA's Transiting Exoplanet Survey Satellite (TESS) mission is expected to
discover hundreds of planets via single transits first identified in their
light curves. Determining the orbital period of these single transit candidates
typically requires a significant amount of follow-up work to observe a second
transit or measure a radial velocity orbit. In Yao et al. (2019), we developed
simulations that demonstrated the ability to use archival photometric data in
combination with TESS to "precover" the orbital period for these candidates
with a precision of several minutes, assuming circular orbits. In this work, we
incorporate updated models for TESS single transits, allowing for eccentric
orbits, along with an updated methodology to improve the reliability of the
results. Additionally, we explore how radial velocity (RV) observations can be
used to follow up single transit events, using strategies distinct from those
employed when the orbital period is known. We find that the use of an estimated
period based on a circular orbit to schedule reconnaissance RV observations can
efficiently distinguish eclipsing binaries from planets. For candidates that
pass reconnaissance RV observations, we simulate RV monitoring campaigns that
enable one to obtain an approximate orbital solution. We find this method can
regularly determine the orbital periods for planets more massive than 0.5 M_J
with orbital periods as long as 100 days.
