We present a user study analyzing head-gaze-based robot control and foveated visual augmentation in a simulated search-and-rescue task. Results show that foveated augmentation significantly improves task performance, reduces cognitive load by 38%, and shortens task time by over 60%. Head-gaze patterns analysed over both the entire task duration and shorter time segments show that near and far attention capture is essential to better understand user intention in critical scenarios. Our findings highlight the potential of foveation as an augmentation technique and the need to further study gaze measures to leverage them during critical tasks.