Saccades represent decisions, and the study of their latency has led to a neurally plausible model of the underlying mechanisms, LATER, that can successfully predict reaction time behaviour in simple decision tasks, with fixed instructions. But if the instructions abruptly change, we have a more complex situation, known as task switching. Psychologists' explanations of the phenomena of task switching have so far tended to be qualitative rather than quantitative, and not intended to relate particularly clearly to existing models of decision making or to likely neural implementations. Here, we investigated task switching using a novel saccadic task: we presented the instructions via stimulus elements identical to those of the task itself, allowing us to compare decisions about instructions with decisions in the actual task. Our results support a relatively simple model consisting of two distinct LATER processes in series: the first detects the instruction, the second implements it.