Metal oxide resistive switches are increasingly important as possible artificial synapses in next-generation neuromorphic networks. Nevertheless, there is still no codified set of tools for studying properties of the devices. To this end, we demonstrate electron beam-induced current measurements as a powerful method to monitor the development of local resistive switching in TiO2-based devices. By comparing beam energy-dependent electron beam-induced currents with Monte Carlo simulations of the energy absorption in different device layers, it is possible to deconstruct the origins of filament image formation and relate this to both morphological changes and the state of the switch. By clarifying the contrast mechanisms in electron beam-induced current microscopy, it is possible to gain new insights into the scaling of the resistive switching phenomenon and observe the formation of a current leakage region around the switching filament. Additionally, analysis of symmetric device structures reveals propagating polarization domains.