Coulomb crystals have proven to be powerful and versatile tools for the study of ion-molecule reactions under cold and controlled conditions. Reactions in Coulomb crystals are typically monitored through a combination of in situ fluorescence imaging of the laser-cooled ions and destructive time-of-flight mass spectrometry measurements of the ejected ions. However, neither of these techniques is able to provide direct structural information on the positions of nonfluorescing "dark" ions within the crystal. In this work, structural information is obtained using a phosphor screen and a microchannel plate detector in conjunction with a Timepix3 camera. The Timepix3 camera simultaneously records the spatial and temporal distribution of all ions that strike the phosphor screen detector following crystal ejection at a selected reaction time. A direct comparison can be made between the observed Timepix3 ion distributions and the distributions established from SIMION simulations of the ion trajectories through the apparatus and onto the detector. Quantitative agreement is found between the measured Timepix3 signal and the properties of Coulomb crystals assigned using fluorescence imaging─independently confirming that the positions and numbers of nonfluorescing ions within Coulomb crystals can be accurately determined using molecular dynamics simulations. It is anticipated that the combination of high-resolution spatial and temporal data will facilitate new measurements of the ion properties within Coulomb crystals.