  The type-II seesaw mechanism with an isospin-triplet scalar $\Delta_L$
provides one of the most compelling explanations for the observed smallness of
neutrino masses. The triplet contains a doubly-charged component
$H_L^{\pm\pm}$, which dominantly decays to either same-sign dileptons or to a
pair of $W$ bosons, depending on the size of the triplet vacuum expectation
value. However, there exists a range of Yukawa couplings $f_L$ of the triplet
to the charged leptons, wherein a relatively light $H_L^{\pm\pm}$ tends to be
long-lived, giving rise to distinct displaced-vertex signatures at the
high-energy colliders. We find that the displaced vertex signals from the
leptonic decays $H_L^{\pm\pm} \to \ell_\alpha^\pm \ell_\beta^\pm$ could probe a
broad parameter space with $10^{-10} \lesssim |f_L| \lesssim 10^{-6}$ and 45.6
GeV $< M_{H_L^{\pm\pm}} \lesssim 200$ GeV at the high-luminosity LHC. Similar
sensitivity can also be achieved at a future 1 TeV $e^+e^-$ collider. The mass
reach can be extended to about 500 GeV at a future 100 TeV proton-proton
collider. Similar conclusions apply for the right-handed triplet $H_R^{\pm\pm}$
in the TeV-scale left-right symmetric models, which provide a natural embedding
of the type-II seesaw. We show that the displaced vertex signals are largely
complementary to the prompt same-sign dilepton pair searches at the LHC and the
low-energy, high-intensity/precision measurements, such as neutrinoless double
beta decay, charged lepton flavor violation, electron and muon anomalous
magnetic moments, muonium oscillation and M{\o}ller scattering.
