Stochastic accumulator models account for response time in perceptual decision-making tasks by assuming that perceptual evidence accumulates to a threshold. The present investigation mapped the firing rate of frontal eye field (FEF) visual neurons onto perceptual evidence and the firing rate of FEF movement neurons onto evidence accumulation to test alternative models of how evidence is combined in the accumulation process. The models were evaluated on their ability to predict both response time distributions and movement neuron activity observed in monkeys performing a visual search task. Models that assume gating of perceptual evidence to the accumulating units provide the best account of both behavioral and neural data. These results identify discrete stages of processing with anatomically distinct neural populations and rule out several alternative architectures. The results also illustrate the use of neurophysiological data as a model selection tool and establish a novel framework to bridge computational and neural levels of explanation.