<p>In the context of future electron-ion collision experiments, particularly the Electron-Ion Collider (EIC) and the Electron-Ion Collider in China (EicC), investigating exclusive photoproduction processes is of paramount importance. These processes offer a distinctive opportunity to probe the gluon structure of nuclei across a broad range of Bjorken <i>x</i>, thereby enabling measurements of nuclear shadowing and facilitating the search for gluon saturation and color glass condensates. This study explores the potential of utilizing neutron tagging via the Coulomb excitation of nuclei to precisely determine the impact parameter for exclusive photoproduction in electron-ion collisions. By developing the equivalent photon approximation for fast electrons, this study incorporates a coordinate-space-dependent photon flux distribution to elucidate the relationship between the photon transverse momentum distribution and the collision impact parameter. Furthermore, the differential cross section for Coulomb excitation of nuclei is derived by leveraging the spatial information from the photon flux. Our calculations demonstrate that neutron tagging can significantly alter the impact parameter distributions, thereby providing a robust method for impact parameter manipulation in electron-ion collisions. This study provides valuable insights and strategies for exploring the impact parameter dependence of exclusive photoproduction, offering novel insights for experimental design and data analysis. Ultimately, it enhances our understanding of the gluon distribution within the nucleus.</p>