Right-handed weak currents (RHCs) in the left-right symmetric model for neutrinoless double beta decays (DBDs) of both the $0^{+}\to 0^{+}$ and $0^{+}\to 2^{+}$ transitions are discussed from both theoretical and experimental viewpoints. $\langle \lambda \rangle$ and $\langle \eta \rangle$ terms are related by $\langle \lambda \rangle /\langle \eta \rangle \approx tan\beta$, which is constrained in the regions of 1–60 for SUSY grand unified theories (GUTs) and of 1–165 for non-SUSY GUTs. The enhancement mechanisms of the $\langle \eta \rangle$ term over the $\langle \lambda \rangle$ term in the $0^{+}$ transition is shown, and the $\mathrm{\Delta }$ isobar contribution to the nuclear matrix element (NME) for the transition to the $2^{+}$ state is found to be of the order of $20\%$ of the NME with the quenched weak coupling. The new and interesting RHC regions of $\langle \lambda \rangle \approx 5\times {10}^{-8}$ and $\langle \eta \rangle \approx 1.5\times {10}^{-10}$ are shown to be exclusively explored by measuring both the $\beta \beta$ and $\gamma$ rays associated with the ground and excited DBDs by means of the ton-scale DBD detectors for the inverted hierarchy $\nu$ masses. The actual RHCs to be studied depend on the RHC NMEs.