Kerr cavities driven in the normal dispersion regime are known to host switching waves. These consist of a traveling wavefront that connects separate regions associated with high- and low-intensity steady states of the cavity. In this Letter, we drive a 230-m custom built fiber ring cavity with strong normal dispersion using nanosecond pulses, allowing us to directly resolve the fine structure of individual switching waves, including resonant oscillations occurring over periods of the order of ∼10 ps. We demonstrate the intimate connection between the temporal and spectral features of the dispersive waves associated with switching waves, while also investigating how these dispersive waves evolve with cavity parameters, namely the frequency detuning and pump desynchronization. Furthermore, by applying a localized and temporary perturbation to our driving field in the presence of a phase modulation trapping potential, we are able to generate a stable and persistent dark pulse, allowing us to directly observe and model the interlocking of two stationary switching waves under quasi-CW pumping conditions. These results further verify the accuracy of the dispersive wave formalism used, and show that their temporal modulation frequency and decay rate in a pulsed-pumped cavity are accurately captured from theory previously applied to CW-pumped systems.