The drift diffusion model predicts that variability in response time (RT) is primarily due to the time required for evidence to stochastically accumulate to a response boundary. Total RT depends on both the quality of perceptual processing output (the mean rate of accumulation), and also the duration of perceptual processing (the delay from stimulus to start of accumulation). The activity of movement neurons in the frontal eye field (FEF) is associated with a stochastic accumulation; these cells initiate a saccade when activity reaches a fixed threshold. During saccade visual search, the onset of movement neuron activity correlates with RT, and increases when search is more difficult. This suggests that the duration of perceptual processing was increased. We simulated trajectories using various forms of the drift diffusion model and measured the onset with the same analyses used to detect the onset of neurophysiological activity. We found that varying the rate of accumulation resulted in large changes in the measured onset of model trajectories even when the start of the accumulation was fixed. These results show that a correlation between the onset of neural activity and RT alone is not sufficient to conclude that changes in RT were due to changes in the duration, but not quality, of perceptual processing.