  In this article, we study an almost contact metric structure on a
$G_2$-manifold constructed by Arikan, Cho and Salur in via the classification
of almost contact metric structures given by Chinea and Gonzalez. In
particular, we characterize when this almost contact metric structure is
cosymplectic and narrow down the possible classes in which this almost contact
metric structure could lie. Finally, we show that any closed $G_2$-manifold
admits an almost contact metric $3$-structure by constructing it explicitly and
characterize when this almost contact metric $3$-structure is $3$-cosymplectic.
