  We study the four-dimensional low energy effective $\mathcal{N}=1$
supergravity theory of the dimensional reduction of M-theory on
$G_2$-manifolds, which are constructed by Kovalev's twisted connected sum
gluing suitable pairs of asymptotically cylindrical Calabi-Yau threefolds
$X_{L/R}$ augmented with a circle $S^1$. In the Kovalev limit the Ricci-flat
$G_2$-metrics are approximated by the Ricci-flat metrics on $X_{L/R}$ and we
identify the universal modulus - the Kovalevton - that parametrizes this limit.
We observe that the low energy effective theory exhibits in this limit gauge
theory sectors with extended supersymmetry. We determine the universal
(semi-classical) K\"ahler potential of the effective $\mathcal{N}=1$
supergravity action as a function of the Kovalevton and the volume modulus of
the $G_2$-manifold. This K\"ahler potential fulfills the no-scale inequality
such that no anti-de-Sitter vacua are admitted. We describe geometric
degenerations in $X_{L/R}$, which lead to non-Abelian gauge symmetries
enhancements with various matter content. Studying the resulting gauge theory
branches, we argue that they lead to transitions compatible with the gluing
construction and provide many new explicit examples of $G_2$-manifolds.
