  In topological insulator edges, the duality between the Zeeman field
orientation and the proximitized superconducting phase has been recently
exploited to predict a magneto-Josephson effect with a 4$\pi$ periodicity. We
revisit this latter Josephson effect in the light of this duality and show that
the same 4$\pi$ quantum anomaly occurs when bridging two spinless Thouless
pumps to a p-wave superconducting region that could be as small as a single and
experimentally-relevant superconducting quantum dot - a point-like defect. This
interpretation as a dual Josephson effect never requires the presence of
Majorana modes but rather builds on the topological properties of adiabatic
quantum pumps with Z topological invariants. It allows for the systematic
construction of dual Josephson effects of arbitrary periodicity, such as 4$\pi$
and 8$\pi$, by using point-like defects whose symmetry differs from that of the
pump, dubbed symmetry defects. Although adiabatic quantum pumps are typically
discussed via mappings to two-dimensional geometries, we show that this
phenomenology does not have any counterpart in conventional two-dimensional
systems.
