  Charge separation ($\Delta S$) measurements, obtained relative to the
$2^{\rm{nd}}$-order ($\Psi_2$) and $3^{\rm{rd}}$-order ($\Psi_3$) event planes
with a new charge-sensitive correlator ${R_{\Psi_m}(\Delta S)}$, are presented
for $p$($d$)+Au and Au+Au collisions at $\sqrt{s_{NN}}=200$~GeV. The
correlator, which is sensitive to the hypothesized Chiral Magnetic Effect
(CME), show the expected patterns of background-driven charge separation for
the measurements relative to $\Psi_3$ and those relative to $\Psi_2$ for the
$p$($d$)+Au systems. By contrast, the Au+Au measurements relative to $\Psi_2$,
show event-shape-independent ${R_{\Psi_2}(\Delta S)}$ distributions consistent
with a CME-driven charge separation, quantified by widths having an inverse
relationship to the Fourier dipole coefficient $\tilde{a}_1$, which evaluates
the CME. The extracted values of these widths and their dependencies on
centrality and event-shape give new constraints for possible CME-driven charge
separation in relativistic heavy-ion collisions.
