We interpret the 2 TeV excesses at the LHC in a left-right symmetric model with Higgs doublets and spontaneous $D$-parity violation. The light neutrino masses are understood via a linear seesaw, suppressed by a high $D$-parity breaking scale, and the heavy neutrinos have a pseudo-Dirac character. In addition, with a suppressed right-handed gauge coupling $g_R / g_L approx 0.6$ in an $SO(10)$ embedding, we can thereby interpret the observed $eejj$ excess at CMS. We show that it can be reconciled with the diboson and dijet excesses within a simplified scenario based on our model. Moreover, we find that the mixing between the light and heavy neutrinos can be potentially large which would induce dominant non-standard contributions to neutrinoless double beta decay via long-range $lambda$ and $eta$ neutrino exchange.
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