  We examine the taste structure of eigenvectors of the staggered-fermion Dirac
operator. We derive a set of conditions on the eigenvectors of modes with small
eigenvalues (near-zero modes), such that staggered fermions reproduce the 't
Hooft vertex in the continuum limit. We also show that, assuming these
conditions, the correlators of flavor-singlet mesons are free of contributions
singular in $1/m$, where $m$ is the quark mass. This conclusion holds also when
a single flavor of sea quark is represented by the fourth root of the
staggered-fermion determinant. We then test numerically, using the HISQ action,
whether these conditions hold on realistic lattice gauge fields. We find that
the needed structure does indeed emerge.
