Inducing the rubber hand illusion (RHI) requires that participants look at an imitation hand while it is stroked in synchrony with their occluded biological hand. Previous explanations of the RHI have emphasized multisensory integration, and excluded higher cognitive functions. We investigated the relationship between the RHI and higher cognitive functions by experimentally testing task switch (as measured by switch cost) and mind wandering (as measured by SART score); we also included a questionnaire for attentional control that comprises two subscales, attention-shift and attention-focus. To assess experience of RHI, the Botvinick and Cohen (1998) questionnaire was used and illusion onset time was recorded. Our results indicate that rapidity of onset reliably indicates illusion strength. Regression analysis revealed that participants evincing less switch cost and higher attention-shift scores had faster RHI onset times, and that those with higher attention-shift scores experienced the RHI more vividly. These results suggest that the multi-sensory hypothesis is not sufficient to explain the illusion: higher cognitive functions should be taken into account when explaining variation in the experience of ownership for the rubber hand.