We study the diffractive dissociation of a virtual photon in the scattering off a large nucleus at high energies in the QCD dipole picture in which the photon is conveniently represented by an onium. In a well-defined parametric regime, the nuclear scattering of the onium is triggered by large-dipole fluctuations in the course of its rapidity evolution in the form of color dipole branching, and the diffractive dissociation with a minimal gap $Y_0$ is tantamount to the probability that an even number of the dipoles in the onium Fock state effectively participates in the scattering, in a frame in which the onium is evolved to the rapidity $Y−Y_0$ out of the total relative rapidity $Y$. Such picture allows to extract the asymptotic solution to the Kovchegov-Levin equation, established in QCD 20 years ago, which rules the diffractive cross section. Diffraction in electron-ion collisions, which can be linked to the same process in onium-nucleus scattering, is then studied based on numerical solutions of the original Kovchegov-Levin equation and of its next-to-leading extension taking into account the running of the strong coupling, with the aim to make predictions for the distribution of rapidity gaps in realistic kinematics of future electron-ion colliders. We show that the fixed and the running coupling equations lead to different distributions, rather insensitive to the chosen prescription in the running coupling case. The obtained distributions for the fixed coupling framework exhibit a shape characteristic of the above-mentioned picture already at rapidities accessible at future electron-ion colliders, which demonstrates the relevance of measurements of such observables for the microscopic understanding of diffractive dissociation in QCD.