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By fibering the duality between the $E_{8}\times E_{8}$ heterotic string on$T^{3}$ and M-theory on K3, we study heterotic duals of M-theory compactifiedon $G_{2}$ orbifolds of the form $T^{7}/\mathbb{Z}_{2}^{3}$. While theheterotic compactification space is straightforward, the description of thegauge bundle is subtle, involving the physics of point-like instantons onorbifold singularities. By comparing the gauge groups of the dual theories, wededuce behavior of a "half-$G_{2}$" limit, which is the M-theory analog of thestable degeneration limit of F-theory. The heterotic backgrounds exhibitpoint-like instantons that are localized on pairs of orbifold loci, similar tothe "gauge-locking" phenomenon seen in Ho\v{r}ava-Witten compactifications. Inthis way, the geometry of the $G_{2}$ orbifold is translated to bundle data inthe heterotic background. While the instanton configuration looks surprisingfrom the perspective of the $E_{8}\times E_{8}$ heterotic string, it may beunderstood as T-dual $\text{Spin}(32)/\mathbb{Z}_{2}$ instantons along withwinding shifts originating in a dual Type I compactification.

Non-Perturbative Heterotic Duals of M-Theory on $G_{2}$ Orbifolds