  A linear Josephson junction mediated by the surface states of a
time-reversal-invariant Weyl or Dirac semimetal localizes Majorana flat bands
protected by the time-reversal symmetry. We show that as a result, the
Josephson current exhibits a discontinuous jump at $\pi$ phase difference which
can serve as an experimental signature of the Majorana bands. The magnitude of
the jump scales proportionally to the junction width and the momentum space
distance between the Weyl nodes. It also exhibits a characteristic dependence
on the junction orientation. We demonstrate that the jump is robust against the
effects of non-zero temperature and weak non-magnetic disorder.
