  This paper continues the systematic investigation of diffusive shear
instabilities initiated in Part I of this series. In this work, we primarily
focus on quantifying the impact of non-local mixing, which is not taken into
account in Zahn's mixing model \citep{Zahn92}. We present the results of direct
numerical simulations in a new model setup designed to contain coexisting
laminar and turbulent shear layers. As in Part I, we use the Low P\'eclet
Number approximation of \citet{Lign1999} to model the evolution of the
perturbations. Our main findings are twofold. First, turbulence is not
necessarily generated whenever Zahn's nonlinear criterion \citep{Zahn1974}
$J{\rm Pr} < (J{\rm Pr})_c$ is satisfied, where $J=N^2/S^2$ is the local
gradient Richardson number, ${\rm Pr} = \nu/ \kappa_T$ is the Prandtl number,
and $(J{\rm Pr})_c \simeq 0.007$. We have demonstrated that the presence or
absence of turbulent mixing in this limit hysteretically depends on the history
of the shear layer. Second, Zahn's nonlinear instability criterion only
approximately locates the edge of the turbulent layer, and mixing beyond the
region where $J{\rm Pr} < (J{\rm Pr})_c$ can also take place in a manner
analogous to convective overshoot. We found that the turbulent kinetic energy
decays roughly exponentially beyond the edge of the shear-unstable region, on a
lengthscale $\delta$ that is directly proportional to the scale of the
turbulent eddies, which are themselves of the order of the Zahn scale (see Part
I). Our results suggest that mixing by diffusive shear instabilities should be
modeled with more care than is currently standard in stellar evolution codes.
