Data-driven approaches struggle with precise manipulation: imitation learning requires many hard-to-obtain demonstrations, while reinforcement learning yields brittle, non-generalizable policies. We introduce VisuoTactile Local (VITAL) policy learning, which decomposes fine-grained manipulation into two phases: a reaching phase, where a visionlanguage model (VLM) performs scene-level reasoning to localize the object of interest, and a local manipulation phase, where a reusable, scene-agnostic VITAL policy performs contactrich manipulation using egocentric vision and tactile sensing. This decomposition is motivated by the observation that while scene context varies, the low-level interaction remains consistent across task instances; trained once in a canonical setting, local policies generalize via a localize-then-execute strategy. VITAL achieves ∼90% success on contact-rich tasks in unseen environments and is robust to distractors. Its effectiveness stems from three insights: (1) segmentation foundation models enable training robust visual encoders via behavior cloning; (2) these encoders improve the generalizability of policies learned with residual RL; and (3) tactile sensing significantly boosts performance in contact-rich tasks. Ablations validate each insight, and VITAL integrates well with high-level VLMs, enabling robust, reusable low-level skills. Results and videos are available at anonvital.github.io.