  We study the first hitting time statistics between a one-dimensional
run-and-tumble particle and a target site that switches intermittently between
visible and invisible phases. The two-state dynamics of the target is
independent of the motion of the particle, which can be absorbed by the target
only in its visible phase. We obtain the mean first hitting time when the
motion takes place in a finite domain with reflecting boundaries. Considering
the turning rate of the particle as a tuning parameter, we find that ballistic
motion represents the best strategy to minimize the mean first hitting time.
However, the relative fluctuations of the first hitting time are large and
exhibit non-monotonous behaviours with respect to the turning rate or the
target transition rates. Paradoxically, these fluctuations can be the largest
for targets that are visible most of the time, and not for those that are
mostly invisible or rapidly transiting between the two states. On the infinite
line, the classical asymptotic behaviour $\propto t^{-3/2}$ of the first
hitting time distribution is typically preceded, due to target intermittency,
by an intermediate scaling regime varying as $t^{-1/2}$. The extent of this
transient regime becomes very long when the target is most of the time
invisible, especially at low turning rates. In both finite and infinite
geometries, we draw analogies with partial absorption problems.
