  Several hundreds of thousands of eclipsing binaries (EBs) are expected to be
detected in the Transiting Exoplanet Survey Satellite (TESS) full frame images
(FFIs). This represents a significant increase in the number of EBs available
for eclipse timing variation studies. In this paper, we investigate the
feasibility of performing precise eclipse timing of TESS EBs using the FFIs. To
this end, we developed a fast, automated method and applied it to a sample of
$\sim$100 EBs selected from the Villanova TESS EB catalog. Our timing analysis
resulted in the detection of ten new triple candidates with outer periods
shorter than $\sim$1300$\,$d. For five of them, we were able to constrain the
outer orbit by analyzing independently the short-cadence (SC) and FFI data and
to derive the minimum mass of the third body with a precision better than 4 per
cent for SC and 12 per cent for FFI data. We then compared the results obtained
from the two datasets and found that using the FFI data leads to (1) a
degradation of both the accuracy and precision of the tertiary mass
determination for the tightest EBs and (2) an overall underestimation of the
third component's mass. However, we stress that our main conclusions on the
nature of the detected signals do not depend on which dataset is used. This
confirms the great potential of TESS FFIs, which will allow us to search for
rare objects such as substellar circumbinary companions and compact triple
stellar systems.
