  We point out that in generic TeV scale seesaw models for neutrino masses with
local $B-L$ symmetry breaking, there is a phenomenologically allowed range of
parameters where the Higgs field responsible for $B-L$ symmetry breaking leaves
a physical real scalar field with mass around GeV scale. This particle (denoted
here by $H_3$) is weakly mixed with the Standard Model Higgs field ($h$) with
mixing $\theta_1\lesssim m_{H_3}/m_h$, barring fine-tuned cancellation. In the
specific case when the $B-L$ symmetry is embedded into the TeV scale left-right
seesaw scenario, we show that the bounds on the $h-H_3$ mixing $\theta_1$
become further strengthened due to low energy flavor constraints, thus forcing
the light $H_3$ to be long lived, with displaced vertex signals at the LHC. The
property of left-right TeV scale seesaw models are such that they make the
$H_3$ decay to two photons as the dominant mode. This is in contrast with a
generic light scalar that mixes with the SM Higgs boson, which could also have
leptonic and hadronic decay modes with comparable or larger strength. We
discuss the production of this new scalar field at the LHC and show that it
leads to testable displaced vertex signals of collimated photon jets, which is
a new distinguishing feature of the left-right seesaw model. We also study a
simpler version of the model where the $SU(2)_R$ breaking scale is much higher
than the ${\cal O}$(TeV) $U(1)_{B-L}$ breaking scale, in which case the
production and decay of $H_3$ proceed differently, but its long lifetime
feature is still preserved for a large range of parameters. Thus, the search
for such long-lived light scalar particles provides a new way to probe TeV
scale seesaw models for neutrino masses at colliders.
