The source function (SF) introduced in late 90s by Bader and Gatti quantifies the influence of each atom in a system in determining the amount of electron density at a given point, regardless of the atom's remote or close location with respect to the point. The SF may thus be attractive for studying directly in the real space somewhat elusive molecular properties, such as "electron conjugation" and "aromaticity", that lack rigorous definitions as they are not directly associated to quantum-mechanical observables. In this work, the results of a preliminary test aimed at understanding whether the SF descriptor is capable to reveal electron delocalization effects are corroborated by further examination of the previously investigated benzene, 1,3-cyclohexadiene, and cyclohexene series and by extending the analysis to some benchmark organic systems with different unsaturated bond patterns. The SF can actually reveal, order, and quantify pi-electron delocalization effects for formal double, single conjugated, and allylic bonds, in terms of the influence of distant atoms on the electron density at given bond critical points. In polycyclic aromatic hydrocarbons, the SF neatly reveals the mutual influence of the benzenoid subunits. In naphthalene it provides a rationale for the changes observed in the local aromatic character of one ring when the other is partially hydrogenated. The SF analysis describes instead biphenyl as made up by two weakly interacting benzene rings, only slightly perturbed by the combination of mutual steric and electronic effects. Eventually, a new SF-based indicator of local aromaticity is introduced, which shows excellent correlation with the aromatic index developed by Matta and Hernandez-Trujillo, based on the delocalization indices. At variance with this latter and other commonly employed quantum-mechanical (local) aromaticity descriptors, the SF-based indicator does not require the knowledge of the pair density, nor the system wave function, being therefore promising for applications to experimentally derived charge density distributions.