The three-body fragmentation dynamics of pyridine trications ${\mathrm{C}}_{5}{\mathrm{H}}_{5}{\mathrm{N}}^{3+}$ produced by 200-eV electron-impact triple ionization are investigated using a reaction microscope. The three complete deprotonation fragmentation channels of ${\mathrm{H}}^{+}+{\mathrm{CH}}_{2}{\mathrm{N}}^{+}+{\mathrm{C}}_{4}{\mathrm{H}}_{2}^{+}, {\mathrm{H}}^{+}+{\mathrm{C}}_{2}{\mathrm{H}}_{2}^{+}+{\mathrm{C}}_{3}{\mathrm{H}}_{2}{\mathrm{N}}^{+}$, and ${\mathrm{H}}^{+}+{\mathrm{C}}_{3}{\mathrm{H}}_{2}^{+}+{\mathrm{C}}_{2}{\mathrm{H}}_{2}{\mathrm{N}}^{+}$ are determined by multiparticle coincidence momentum imaging. By analyzing the correlation maps as a function of kinetic energy release and the angle $\ensuremath{\theta}$ between the conjugate momenta of the first and second breakup steps as well as the momentum correlation spectra of three fragment ions (Newton diagram) in these three channels, we separate two distinct sequential mechanisms involving proton emission in the first or second step of sequential fragmentation. Moreover, we determine the relative ratio of the two dissociation pathways for each channel. We find that proton emission in the first step of the sequential dissociation is the dominant process (94% branching ratio) for the channel involving the H migration of ${\mathrm{H}}^{+}+{\mathrm{CH}}_{2}{\mathrm{N}}^{+}+{\mathrm{C}}_{4}{\mathrm{H}}_{2}^{+}$. It can be explained by the pyridine trication undergoing ultrafast hydrogen migration and forming a more stable $\ensuremath{\alpha}$-isomeric ion, which attenuates the ring-opening reactions. Our study provides insight into the dynamics of deprotonation and ring-breaking reactions in the three-body fragmentation processes of heterocyclic molecules.