Interactive workspaces combine horizontal and vertical touch surfaces into a single digital workspace. During an exploration of these systems, it was shown that direct interaction on the vertical surface is cumbersome and more inaccurate than on the horizontal one. To overcome these problems, indirect touch systems turn the horizontal touch surface into the input which allows manipulation of objects on the vertical display. If the horizontal touch surface also acts as a display, however, it becomes necessary to notify the system which screen is currently in use by providing a switching mode. We investigate the use of gaze tracking to perform these mode switches. In three user studies, we compare absolute and relative gaze augmented selection techniques with the traditional direct-touch approach. Our results show that our relative gaze augmented selection technique outperforms the other techniques for simple tapping tasks alternating between horizontal and vertical surfaces, and for dragging on the vertical surface. However, when tasks involve dragging across surfaces, the findings are more complex. We provide a detailed description of the proposed interaction techniques, a statistical analysis of these interaction techniques, and how they can be applied to systems that involve a combination of multiple horizontal and vertical touch surfaces.