  We probed a gate-tunable InAs nanowire Josephson weak link by coupling it to
a microwave resonator. Tracking the resonator frequency shift when the weak
link is close to pinch-off, we observe that the ground state of the latter
alternates between a singlet and a doublet when varying either the gate voltage
or the superconducting phase difference across it. The corresponding microwave
absorption spectra display lines that approach zero energy close to the
singlet-doublet boundaries, suggesting parity flipping transitions, which are
in principle forbidden in microwave spectroscopy and expected to arise only in
tunnel spectroscopy. We tentatively interpret them by means of an ancillary
state isolated in the junction acting as a reservoir for individual electrons.
