Foundation models have driven remarkable progress in text, vision, and video understanding, and are now poised to unlock similar breakthroughs in trajectory modeling. We introduce the GPSMasked Trajectory Transformer (GPS-MTM), a foundation model for large-scale mobility data that captures patterns of normalcy in human movement. Unlike prior approaches that flatten trajectories into coordinate streams, GPS-MTM decomposes mobility into two complementary modalities: states (point-of-interest categories) and actions (agent transitions). Leveraging a bi-directional Transformer with a self-supervised masked modeling objective, the model reconstructs missing segments across modalities, enabling it to learn rich semantic correlations without manual labels. Across benchmark datasets, including Numosim-LA, Urban Anomalies, and Geolife, GPS-MTM consistently outperforms on downstream tasks such as trajectory infilling and next-stop prediction. Its advantages are most pronounced in dynamic tasks (inverse and forward dynamics), where contextual reasoning is critical. These results establish GPS-MTM as a robust foundation model for trajectory analytics, positioning mobility data as a first-class modality for large-scale representation learning. Code is released for further reference.