  We consider a finite-size topological Josephson junction formed at the edge
of a two-dimensional topological insulator in proximity to conventional
superconductors and study the impact of Cooper pair symmetries on the electron
transport. We find that, due to the finite junction size, electron transport is
highly tunable by the superconducting phase difference $\phi$ across the
junction. At zero frequency and $\phi=\pi$, the setup exhibits vanishing local
Andreev reflection and perfect normal transmission due to the interplay of
finite junction size and formation of topological Andreev bound states in the
middle of the junction. We reveal that this striking behavior enables
odd-frequency Cooper pairs to become the only type of pairing inside the
topological junction that contribute to transport. Our paper thus offers a
highly tunable detection scheme for odd-frequency Cooper pairs.
