Hemodynamic recordings from visual cortex contain powerful endogenous task-related responses that may reflect task-related arousal, or "task engagement" distinct from attention. We tested this hypothesis with hemodynamic measurements (intrinsic-signal optical imaging) from monkey primary visual cortex (V1) while the animals' engagement in a periodic fixation task over several hours was varied through reward size and as animals took breaks. With higher rewards, animals appeared more task-engaged; task-related responses were more temporally precise at the task period (approximately 10-20 seconds) and modestly stronger. The 2-5 minute blocks of high-reward trials led to ramp-like decreases in mean local blood volume; these reversed with ramp-like increases during low reward. The blood volume increased even more sharply when the animal shut his eyes and disengaged completely from the task (5-10 minutes). We propose a mechanism that controls vascular tone, likely along with local neural responses in a manner that reflects task engagement over the full range of timescales tested.