Humans and other animals are adept at learning to perform cognitively demanding behavioral tasks. Neurophysiological recordings in nonhuman primates during such tasks find that the requisite cognitive variables are encoded strongly in core oculomotor brain regions. Here, we assembled a large dataset—11 monkeys performing an abstract visual categorization task, surveyed across more than 1,000 neural recording sessions—to reveal that this produces a robust but uninstructed behavioral “tell,” observed in all subjects and experiments: small, cognitively modulated eye movements. We find that these eye movements are causally linked to activity in SC but not LIP, and that they occur following transient alignment of cognitive and saccadic population coding subspaces in SC. This behavioral signature of oculomotor engagement is absent during a similar task that does not require rule-based categorization, suggesting that abstract task behaviors recruit primate oculomotor networks more strongly than previously understood.