  We show that the correlation between the elliptic momentum anisotropy, $v_2$,
and the average transverse momentum, $[p_T]$, at fixed multiplicity in small
system nuclear collisions carries information on the origin of the observed
momentum anisotropy. A calculation using a hybrid
IP-Glasma+\textsc{Music}+UrQMD model that includes contributions from final
state response to the initial geometry as well as initial state momentum
anisotropies of the Color Glass Condensate, predicts a characteristic sign
change of the correlator $\hat{\rho}(v_2^2,[p_T])$ as a function of charged
particle multiplicity in p+Au and d+Au collisions at $\sqrt{s}=200\,{\rm GeV}$,
and p+Pb collisions at $\sqrt{s}=5.02\,{\rm TeV}$. This sign change is absent
in calculations without initial state momentum anisotropies. The model further
predicts a qualitative difference between the centrality dependence of
$\hat{\rho}(v_2^2,[p_T])$ in Au+Au collisions at $\sqrt{s}=200\,{\rm GeV}$ and
Pb+Pb collisions at $\sqrt{s}=5.02\,{\rm TeV}$, with only the latter showing a
sign change in peripheral events. Predictions for O+O collisions at different
collision energy show a similar behavior. Experimental observation of these
distinct qualitative features of $\hat{\rho}(v_2^2,[p_T])$ in small and large
systems would constitute strong evidence for the presence and importance of
initial state momentum anisotropies predicted by the Color Glass Condensate
effective theory.
