While the involvement of executive processes in mind wandering is largely undebated, their exact relationship is subject to an ongoing debate and rarely studied dynamically within-subject. Several brain-stimulation studies using transcranial direct current stimulation (tDCS) have attempted to modulate mind-wandering propensity by stimulating the left dorsolateral prefrontal cortex (DLPFC) which is an important hub in the prefrontal control network. In a series of three studies testing a total of N = 100 participants, we develop a novel task that allows to study the dynamic interplay of mind wandering, behavioural varibility and the flexible recruitment of executive resources as indexed by the randomness (entropy) of movement sequences generated by our participants. We consistently find that behavioural variability is increased and randomness is decreased during periods of mind wandering. Interestingly, we also find that behavioural variability interacts with the entropy-MW effect, opening up the possibility to detect distinct states of off-focus cognition. When applying a high-definition transcranial direct-current stimulation (HD-tDCS) montage to the left DLPFC, we find that propensity to mind wander is reduced relative to a group receiving sham stimulation.