The search for magnetically-induced signatures in ultra-high energy cosmic ray data is a promising path for the identification of their sources. We use data of the Pierre Auger Observatory measured between 2004 and 2018, for two energy thresholds, 20 EeV and 40 EeV, providing unprecedented statistics: the number of cosmic rays included in the analyses for these energy thresholds is above 6500 and 1100, respectively. Two analysis approaches are used. In one, we search for inversely energy-ordered deflection patterns, while in the other we analyze the strength of collimation of energy along the local system of principal axes. We apply the analyses for a targeted search in regions around source candidates of active galactic nuclei and starburst galaxies. In addition, for the energy-ordered patterns an all-sky search has been performed. We also report the performance of the method evaluated using simulated data sets, including deflection in a model of the Galactic magnetic field which includes coherent and turbulent components, and with different composition scenarios.