  In a weak coupling limit the neighborhood of $E_6$ Yukawa points in $SU(5)$
GUT F-theory models is described by a non-resolvable orientifold of the
conifold. We explicitly show, first directly in IIB and then via a mirror
symmetry argument, that in this limit the $E_6$ Yukawa coupling is better
described as coming from the non-perturbative contribution of a euclidean
D1-brane wrapping the non-resolvable cycle. We also discuss how the M-theory
description interpolates between the weak and strong coupling viewpoints.
