  Finding the $F$-theory dual of a Heterotic model with Wilson-line symmetry
breaking presents the challenge of achieving the dual $\mathbb{Z}_{2}$-action
on the $F$-theory model in such a way that the $\mathbb{Z}_{2}$-quotient is
Calabi-Yau with an Enriques $\mathrm{GUT}$ surface over which
$SU\left(5\right)_{gauge}$ symmetry is maintained. We propose a new way to
approach this problem by taking advantage of a little-noticed choice in the
application of Narasimhan-Seshadri equivalence between real $E_{8}$-bundles
with Yang-Mills connection and their associated complex holomorphic
$E_{8}^{\mathbb{C}}$-bundles, namely the one given by the real outer
automorphism of $E_{8}^{\mathbb{C}}$ by complex conjugation. The triviality of
the restriction on the compact real form $E_{8}$ allows one to introduce it
into the $\mathbb{Z}_{2}$-action, thereby restoring $E_{8}$- and hence
$SU\left(5\right)_{gauge}$- symmetry on which the Wilson line can be wrapped.
