  In high energy electron-ion colliders, a new way to probe nucleon structure
becomes available through diffractive reactions, where the incident particle
produces a very energetic almost forward particle. QCD describes these
reactions as due to the exchange of a Pomeron which may be perturbatively
described as a dressed two-gluon state, provided a hard scale allows the
factorization of the amplitude in terms of two impact factors convoluted with a
Pomeron propagator. We consider here a process where such a description allows
to access hadronic structure in terms of the generalized parton distributions,
namely the electroproduction of a forward $\rho$ meson and a timelike deeply
virtual photon, separated by a large rapidity gap. We explore the dependence of
the cross section on the kinematic variables and study the dependence on the
non-perturbative inputs (generalized parton distributions, distribution
amplitude). Our leading order studies show the cross section is mainly
sensitive to the GPD model input, but the small size of the cross sections
could prohibit straightforward analysis of this process at planned facilities.
