This work investigates the role of crystallized layer periodicity and thickness on functional response in chemical solution-deposited lead zirconate titanate thin films fabricated with periodic, alternating Zr and Ti gradients normal to the surface of the film. Films were processed with a range of layer periodicities with similar total film thickness, in order to relate the number of layers and compositional oscillations to structural and functional response changes. Trends of increased extrinsic contributions to the dielectric and ferroelectric responses are observed with increasing layer periodicity, but are counterpointed by simultaneous reductions of intrinsic contributions to the same. Transmission electron microscopy reveals in-plane crystallographic discontinuity at individual crystallization interfaces. Samples with smaller periodicity, and thus thinner layers, potentially suffer from out-of-plane grain size refinement and subsequent reduction in domain size, thereby limiting potential extrinsic contributions to the response. The strong compositional oscillations in samples with larger periodicity result in deep fluctuations to the tetragonal side of the phase diagram, potentially reducing intrinsic contributions to the response. On the other hand, piezoresponse force microscopy results suggest the large chemical oscillations in samples with larger periodicity also result in closer proximity to the morphotropic phase boundary, as evidenced by local acoustic softening at switching, signaling potential phase transitions.