Gaze is an essential prompt for analyzing human behavior and attention. Recently, there has been an increasing interest in determining gaze direction from facial videos. However, video gaze estimation faces significant challenges, such as understanding the dynamic evolution of gaze in video sequences, dealing with static backgrounds, and adapting to variations in illumination. To address these challenges, we propose a simple and novel deep learning model designed to estimate gaze from videos, incorporating a specialized attention module. Our method employs a spatial attention mechanism that tracks spatial dynamics within videos. This technique enables accurate gaze direction prediction through a temporal sequence model, adeptly transforming spatial observations into temporal insights, thereby significantly improving gaze estimation accuracy. Additionally, our approach integrates Gaussian processes to include individual-specific traits, facilitating the personalization of our model with just a few labeled samples. Experimental results confirm the efficacy of the proposed approach, demonstrating its success in both within-dataset and cross-dataset settings. Specifically, our proposed approach achieves state-of-the-art performance on the Gaze360 dataset, improving by 2.5° without personalization. Further, by personalizing the model with just three samples, we achieved an additional improvement of 0.8°. The code and pre-trained models are available at https://github.com/jswati31/stage.