We have recently augmented the electronics for our neutron monitor (NM) latitude survey so as to record the elapsed time (δT) between detected neutrons in each proportional tube, in order to examine time correlations in the data as a function of cutoff rigidity and primary spectrum. We quantify the dependence of counting rate on dead time, with particular focus on the longer dead times that were once employed in FSU/Russian stations. Our observations show that monitor dead time has little influence on the observed depth of Forbush decreases, indicating that the cosmic ray spectral shape is little changed in the decrease. However, the use of a different dead time significantly alters the response of the monitor as a function of cutoff rigidity. In spite of the general success of our calculation in reproducing the data, unexplained discrepancies are still present.