Mental tasks that feature algorithmic processing with symbolic items are shown to rely on brain regions known for visual-spatial functions. Yet, exactly how these functions may help execution of amodal tasks remains an open question. Here we propose a hypothesis for manipulation of items in working memory, which relies on registering items in a spatially-organized short-term memory store. Switching executive attention to items that need processing may then be embodied through shifting spatial attention towards those registry locations. We studied gaze shifts of human subjects during memory tasks as a proxy for shifts in spatial attention. Analysis of gaze shifts during sorting random sequences of five decimal digits indicates that sorting in memory elicits gaze shifts that correlate with sorting procedure. Our proposal establishes a functional relationship between general-purpose production mechanisms that support algorithmic memory tasks with amodal items, and modal systems for perception and action.