  We demonstrate that the photo-electron counting rate, $P^{(2)}$, measured in
two electron coincidence spectroscopy (2$e$-ARPES) experiments, provides
unprecedented insight into the nature of topological superconductivity. In
particular, we show that the spin dependence of $P^{(2)}$ allows one to detect
superconducting spin-triplet correlations that are induced in a topological
superconductor even in the absence of an associated triplet superconducting
order parameter. This ability to detect spin-triplet correlations allows one to
distinguish between two recently proposed scenarios for the microscopic origin
of topological superconductivity in FeSe$_{0.45}$Te$_{0.55}$. Finally, we show
that $P^{(2)}$ exhibits a characteristic intensity maximum that can be employed
to detect topological phase transitions.
