  Abstract abridged. Eclipsing binary systems provide the opportunity to
measure the fundamental parameters of their component stars in a
stellar-model-independent way. This makes them ideal candidates for testing and
calibrating theories of stellar structure and (tidal) evolution. Even without
spectroscopic follow-up there is often enough information in their photometric
time series to warrant analysis, especially if there is an added value present
in the form of intrinsic variability, such as pulsations. Our goal is to
implement and validate a framework for the homogeneous analysis of large
numbers of eclipsing binary light curves, such as the numerous high-duty-cycle
observations from space missions like TESS. The aim of this framework is to be
quick and simple to run and to limit the user's time investment when obtaining,
amongst other parameters, orbital eccentricities. We developed a new and fully
automated methodology for the analysis of eclipsing binary light curves with or
without additional intrinsic variability. Our method includes a fast iterative
pre-whitening procedure. Orbital and stellar parameters are measured under the
assumption of spherical stars of uniform brightness. We tested our methodology
in two settings: a set of synthetic light curves with known input and the
catalogue of Kepler eclipsing binaries. The synthetic tests show that we can
reliably recover the frequencies and amplitudes of the sinusoids included in
the signal as well as the input binary parameters. Recovery of the tangential
component of eccentricity is the most accurate and precise. Kepler results
confirm a robust determination of orbital periods, with 80.5% of periods
matching the catalogued ones. We present the eccentricities for this analysis
and show that they broadly follow the theoretically expected pattern as a
function of the orbital period.
