  Transient Be/X-ray binary systems, wherein a compact object accretes from a
Be-companion star, can show giant and periastron outbursts. During the decay of
their giant outbursts, some Be/X-ray binaries also show X-ray re-brightenings,
the origin of which is not understood. Recently, we presented the discovery of
a jet from a neutron star Be/X-ray binary, observed during the giant outburst
of Swift J0243.6+6124. Here, we present continued radio monitoring of its
2017/2018 giant outburst decay and a re-brightening of this source. During the
former, we observe a radio flare with a steep radio spectrum, possibly caused
by interactions between discrete ejecta colliding with the pre-existing jet or
the surrounding medium. During the X-ray re-brightening, we observe the radio
jet turning on and off within days. Surprisingly, this re-establishing jet is
as bright in radio as at the peak of the super-Eddington giant outburst,
despite more than two orders of magnitude lower X-ray luminosity. In addition,
the jet is only observed when the X-ray luminosity exceeds approximately
$2\times 10^{36} (D/5\rm kpc)^2$ erg/s. We discuss how such an X-ray threshold
for jet launching might be related to the presence of a magnetic centrifugal
barrier at lower mass accretion rates. We also discuss the implications of our
results for the launch of jets from strongly magnetized neutron stars, and
explore future avenues to exploit the new possibility of coordinated
X-ray/radio studies of neutron star Be/X-ray binaries.
