In this work we investigate the effects of switching from mouse cursor control to gaze-based control in a computerized divided attention game. We conducted experiments with nine participants performing a task that requires continuous focused concentration and frequent shifts of attention. Despite carefully controlling experimental and design aspects, the performance of subjects was considerably impaired when using gaze-based control. The participants were experienced users of the mouse control version of the task, we adjusted the difficulty to the more demanding conditions and selected the parameters of gaze input based on previous research findings. In contrast to our assumptions, experienced users could not get used to gaze-based control in the amount of experiments we performed. Additionally we consider the strategies of users, i.e. their method of problem solving, and found that it is possible to make progress in our task even during a short amount of practice. The results of this study provide evidence that the adoption of interfaces controlled by human eye-gaze in cognitively demanding environments require careful design, proper testing and sufficient user training.