The Trail-Making-Test (TMT) is one of the most widely used neuropsychological tests for assessing executive functions, the brain functions underlying cognitively controlled thought and action. Obtaining a number of test scores at once, the TMT allows to characterize an assortment of executive functions efficiently. Critically, however, as most test scores are derived from test completion times, the scores only provide a summary measure of various cognitive control processes. To address this problem, we extended the TMT in two ways. First, using a computerized eye-tracking version of the TMT, we added specific eye movement measures that deliver a richer set of data with a higher degree of cognitive process specificity. Second, we included an experimental manipulation of a fundamental executive function, namely participants' ability to emphasize speed or accuracy in task performance. Our study of healthy participants showed that eye movement measures differed between TMT conditions that are usually compared to assess the cognitive control process of alternating between task sets for action control. This demonstrates that eye movement measures are indeed sensitive to executive functions implicated in the TMT. Crucially, comparing performance under cognitive control sets of speed vs. accuracy emphasis revealed which test scores primarily varied due to this manipulation (e.g., trial duration, number of fixations), and which were still more sensitive to other differences between individuals (e.g., fixation duration, saccade amplitude). This provided an experimental construct validation of the test scores by distinguishing scores primarily reflecting the executive function of emphasizing speed vs. accuracy and those independent from it. In sum, both the inclusion of eye movement measures and of the experimental manipulation of executive functions in the TMT enabled a more specific interpretation of the TMT in terms of cognitive functions and mechanisms, which offers more precise diagnoses in clinical applications and basic research.