Despite remarkable advancements, mainstream gaze estimation techniques, particularly appearance-based methods, often suffer from performance degradation in uncontrolled environments due to variations in illumination and individual facial attributes. Existing domain adaptation strategies, limited by their need for target domain samples, may fall short in real-world applications. This letter introduces Branch-out Auxiliary Regularization (BAR), an innovative method designed to boost gaze estimation's generalization capabilities without requiring direct access to target domain data. Specifically, BAR integrates two auxiliary consistency regularization branches: one that uses augmented samples to counteract environmental variations, and another that aligns gaze directions with positive source domain samples to encourage the learning of consistent gaze features. These auxiliary pathways strengthen the core network and are integrated in a smooth, plug-and-play manner, facilitating easy adaptation to various other models. Comprehensive experimental evaluations on four cross-dataset tasks demonstrate the superiority of our approach.