Schema linking is a difficult and important step in large-scale Text-to-SQL, where systems must identify a compact yet sufficient schema context from large and ambiguous databases. Existing methods often treat schema linking as deterministic selection around a single SQL path, but complex questions may admit multiple valid realizations with different schema needs. We reframe schema linking as uncertainty-aware schema-need inference over multiple plausible SQL paths, where the system distinguishes required schema items from path-dependent uncertain ones and acquires evidence only where needed. We instantiate this reframing with EviLink, which combines multi-hypothesis schema grounding with uncertainty-guided evidence acquisition. Experiments on BIRD-Dev and Spider2-Snow show that this perspective improves the balance among schema completeness, schema relevance, and token cost. On Spider2-Snow, EviLink achieves 90.15% field-level strict recall rate, uses 123.30K average tokens, and improves downstream SQL generation under a fixed generator.