  A gauged $U(1)_X$ extension of the Standard Model is a simple and consistent
framework to naturally incorporate three right-handed neutrinos (RHNs) for
generating the observed light neutrino masses and mixing by the type-I seesaw
mechanism. We examine the collider testability of the $U(1)_X$ model, both in
its minimal form with the conventional charges, as well as with an alternative
charge assignment, via the resonant production of the $U(1)_X$ gauge boson
($Z^\prime$) and its subsequent decay into a pair of RHNs. We first derive an
updated upper limit on the new gauge coupling $g_X$ as a function of the
$Z'$-boson mass from the latest LHC dilepton searches. Then we identify the
maximum possible cross section for the RHN pair-production under these
constraints. Finally, we investigate the possibility of having one of the RHNs
long-lived, even for a TeV-scale mass. Employing the general parametrization
for the light neutrino mass matrix to reproduce the observed neutrino
oscillation data, we perform a parameter scan and find a simple formula for the
maximum RHN lifetime as a function of the lightest neutrino mass eigenvalue
($m_{\rm lightest}$). We find that for $m_{\rm lightest}\lesssim 10^{-5}$ eV,
one of the RHNs in the minimal $U(1)_X$ scenario can be long-lived with a
displaced-vertex signature which can be searched for at the LHC and/or with a
dedicated long-lived particle detector, such as MATHUSLA. In other words, once
a long-lived RHN is observed, we can set an upper bound on the lightest
neutrino mass in this model.
