Applications such as solid-state waste-heat energy conversion, infrared sensing, and thermally-driven electron emission rely on pyroelectric materials (a subclass of dielectric piezoelectrics) which exhibit temperature-dependent changes in polarization. Although enhanced dielectric and piezoelectric responses are typically found at polarization instabilities such as temperature- and chemically-induced phase boundaries, large pyroelectric effects have been primarily limited in study to temperature-induced phase boundaries. Here, we directly identify the magnitude and sign of the intrinsic, extrinsic, dielectric, and secondary pyroelectric contributions to the total pyroelectric response as a function of chemistry in thin films of the canonical ferroelectric PbZr1-xTixO3 (x = 0.40, 0.48, 0.60, and 0.80) across the morphotropic phase boundary. Using phase-sensitive frequency and applied dc-bias methods, the various pyroelectric contributions were measured. It is found that the total pyroelectric response decreases systematically as one moves from higher to lower titanium contents. This arises from a combination of decreasing intrinsic response (-232 μC m-2 K-1 to -97 μC m-2 K-1) and a sign inversion (33 μC m-2 K-1 to -17 μC m-2 K-1) of the extrinsic contribution upon crossing the morphotropic phase boundary. Additionally, the measured secondary and dielectric contributions span between -70 and -29 μC m-2 K-1 and 10-115 μC m-2 K-1 under applied fields, respectively, following closely trends in the piezoelectric and dielectric susceptibility. These findings and methodologies provide novel insights into the understudied realm of pyroelectric response.