Video capsule endoscopy has become increasingly important for investigating the small intestine within the gastrointestinal tract. However, a persistent challenge remains the short battery lifetime of such compact sensor edge devices. Integrating artificial intelligence can help overcome this limitation by enabling intelligent real-time decision-making, thereby reducing the energy consumption and prolonging the battery life. However, this remains challenging due to data sparsity and the limited resources of the device restricting the overall model size. In this work, we introduce a multi-task neural network that combines the functionalities of precise self-localization within the gastrointestinal tract with the ability to detect anomalies in the small intestine within a single model. Throughout the development process, we consistently restricted the total number of parameters to ensure the feasibility to deploy such model in a small capsule. We report the first multi-task results using the recently published Galar dataset, integrating established multi-task methods and Viterbi decoding for subsequent time-series analysis. This outperforms current single-task models and represents a significant advance in AI-based approaches in this field. Our model achieves an accuracy of 93.63% on the localization task and an accuracy of 87.48% on the anomaly detection task. The approach requires only 1 million parameters while surpassing the current baselines.