By tuning the magnetic flux, the two ends of a 1D topological superconductor weakly coupled to a normal metal as a ring-shaped junction can host split Majorana zero modes (MZMs). When this ring geometry becomes Coulomb blockaded, and the two leads come into contact with the two wire ends, the current moves through the superconductor or the normal metal as an interferometer. The two-terminal interference conductance can be experimentally measured as a function of gate voltage and magnetic flux through the ring. However, a 4 pi periodicity in the conductance-phase relation (often considered the hallmark of MZMs), which can arise both in a topological superconductor and in a trivial metal, cannot establish the existence of MZMs. We show that the trivial metal phase can be ruled out in favor of a topological superconductor by studying persistent conductance distribution patterns. In particular, in the presence of MZMs, the conductance peak spacings of the Coulomb blockaded junction would manifest line crossings as the magnetic flux varies. The locations of the line crossings can distinguish line crossings stemming from the trivial metal.