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. Simultaneously, we analyze 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 the 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 unusual, resonant behavior 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∘), 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; 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.