In complex visuomotor tasks, such as cooking, people make many saccades to continuously search for items before and during reaching movements. These tasks require cognitive resources, such as short-term memory and task-switching. Cognitive load may impact limb motor performance by increasing demands on mental processes, but mechanisms remain unclear. The Trail-Making Tests, in which participants sequentially search for and make reaching movements to 25 targets, consist of a simple numeric variant (Trails-A) and a cognitively challenging variant that requires alphanumeric switching (Trails-B). We have previously shown that stroke survivors and age-matched controls make many more saccades in Trails-B, and those increases in saccades are associated with decreases in speed and smoothness of reaching movements. However, it remains unclear how patients with neurological injuries, e.g., stroke, manage progressive increases in cognitive load during visuomotor tasks, such as the Trail-Making Tests. As Trails-B trial progresses, switching between numbers and letters leads to progressive increases in cognitive load. Here, we show that stroke survivors with damage to frontoparietal areas and age-matched controls made more saccades and had longer fixations as they progressed through the 25 alphanumeric targets in Trails-B. Furthermore, when stroke survivors made saccades during reaching movements in Trails-B, their movement speed slowed down significantly. Thus, damage to frontoparietal areas serving cognitive motor functions may cause interference between oculomotor, visual, and limb motor functions, which could lead to significant disruptions in activities of daily living. These findings augment our understanding of the mechanisms that underpin cognitive-motor interference during complex visuomotor tasks.