On the symmetric space for $G_2$, there exist various submanifolds $G_D$ corresponding to the stabilizer of a norm $D$ vector. We show that when a suitable automorphic form is integrated against the $G_D$, the resulting numbers assemble to give a half-integral weight classical modular form. Although this is already implied by a result of Kudla-Millson, we give a simpler proof that avoids the complications in their paper.