Remapping of gaze-centered target-position signals across saccades has been observed in the superior colliculus and several cortical areas. It is generally assumed that this remapping is driven by saccade-related signals. What is not known is how the different potential forms of this signal (i.e., visual, visuomotor, or motor) might influence this remapping. We trained a three-layer recurrent neural network to update target position (represented as a 'hill' of activity in a gaze-centered topographic map) across saccades, using discrete time steps and backpropagation-through-time algorithm. Updating was driven by an efference copy of one of three saccade-related signals: a transient visual response to the saccade-target in 2-D topographic coordinates (Vtop), a temporally-extended motor burst in 2-D topographic coordinates (Mtop), or a 3-D eye velocity signal in brainstem coordinates (EV). The Vtop model produced pre-saccadic remapping in the output layer, with a 'jumping hill' of activity and intra-saccadic suppression. The Mtop model also produced pre-saccadic remapping, with a dispersed moving 'hill' of activity that closely reproduced the quantitative results of Sommer and Wurtz (2006). The EV model produced a coherent moving 'hill' of activity, but failed to produce pre-saccadic remapping. When eye velocity and a topographic (Vtop or Mtop) updater signal were used together, the remapping relied primarily on the topographic signal. An analysis of the hidden layer activity revealed that the transient remapping was highly dispersed across hidden-layer units in both Vtop and Mtop models but tightly clustered in the EV model. These results show that the nature of the updater signal influences both the mechanism and final dynamics of remapping. Taken together with the currently known physiology, our simulations suggest that different brain areas might rely on different signals and mechanisms for updating that should be further distinguishable through currently available single- and multi-unit recording paradigms.