Studies of driving and sleepiness indicators have mainly focused on prior sleep reduction. The present study sought to identify sleepiness indicators responsive to several potential regulators of sleepiness: sleep loss, time of day (TOD) and time on task (TOT) during simulator driving. Thirteen subjects drove a high-fidelity moving base simulator in six 1-h sessions across a 24-h period, after normal sleep duration (8 h) and after partial sleep deprivation (PSD; 4 h). The results showed clear main effects of TOD (night) and TOT but not for PSD, although the latter strongly interacted with TOD. The most sensitive variable was subjective sleepiness, the standard deviation of lateral position (SDLAT) and measures of eye closure [duration, speed (slow), amplitude (low)]. Measures of electroencephalography and line crossings (LCs) showed only modest responses. For most variables individual differences vastly exceeded those of the fixed effects, except for subjective sleepiness and SDLAT. In a multiple regression analysis, SDLAT, amplitude/peak eye-lid closing velocity and blink duration predicted subjective sleepiness bouts with a sensitivity and specificity of about 70%, but were mutually redundant. The prediction of LCs gave considerably weaker, but similar results. In summary, SDLAT and eye closure variables could be candidates for use in sleepiness-monitoring devices. However, individual differences are considerable and there is need for research on how to identify and predict individual differences in susceptibility to sleepiness.