  In this work, we search for observational evidence of higher-order secular
perturbations in three eclipsing binaries. These are slightly eccentric
binaries, and they form the inner pairs of tight, compact, hierarchical triple
star systems. We analyze simultaneously the high precision satellite ($Kepler$
and $TESS$) light curves, eclipse timing variations, combined spectral energy
distributions (through catalog passband magnitudes) and, where available,
radial velocities of KICs 9714358, 5771589 and TIC 219885468. Besides the
determination of robust astrophysical and dynamical properties of the three
systems, we find evidence that the observed unusual eclipse timing variations
of KIC 9714358 are a direct consequence of the octupole-order secular
eccentricity perturbations forced by an unusual, resonant behaviour between the
lines of the apsides of the inner and outer orbital ellipses. We also show
that, despite its evident cyclic eclipse depth variations, KIC~5771589 is an
almost perfectly coplanar system (to within $0.3^\circ$), and we explain the
rapid eclipse depth variations with the grazing nature of the eclipses.
Finally, we find that the inner pair of TIC~219885468 consists of two twin
stars and, hence, in this triple there are no octupole order three-body
perturbations. Moreover, we show that this triple is also coplanar on the same
level as the former one, but due to its deep eclipses, it does not exhibit
eclipse depth variations. We intend to follow this work up with further
analyses and a quantitative comparison of the theoretical and the observed
perturbations.
