  While the phenomenon of gluon nuclear shadowing at small $x$ has been getting
confirmation in QCD analyses of various LHC measurements involving heavy
nuclei, it has not been possible so far to establish experimentally the number
of target nucleons responsible for nuclear shadowing in a given process. To
address this issue, we study coherent $J / \psi$ electroproduction on $^4$He
and $^3$He in the kinematics of a future electron-ion collider and show that
this process has the power to disentangle the contributions of the interaction
with a specific number of nucleons $k$, in particular, with two nucleons at the
momentum transfer $t \neq 0$. We predict a dramatic shift of the $t$-dependence
of the differential cross section toward smaller values of $|t|$ due to a
non-trivial correlation between $x$ and $k$. This calculation, which makes use
for the first time of realistic wave functions, provides a stringent test of
models of nuclear shadowing and a novel probe of the 3D imaging of gluons in
light nuclei. In addition, thanks to this analysis, unique information on the
real part of the corresponding scattering amplitude could be accessed.
