Eye gaze is compelling for interaction with situated displays as we naturally use our eyes to engage with them. In this work we present SideWays, a novel person-independent eye gaze interface that supports spontaneous interaction with displays: users can just walk up to a display and immediately interact using their eyes, without any prior user calibration or training. Requiring only a single off-the-shelf camera and lightweight image processing, SideWays robustly detects whether users attend to the centre of the display or cast glances to the left or right. The system supports an interaction model in which attention to the central display is the default state, while "sidelong glances" trigger input or actions. The robustness of the system and usability of the interaction model are validated in a study with 14 participants. Analysis of the participants' strategies in performing different tasks provides insights on gaze control strategies for design of SideWays applications.