Long-video understanding (LVU) is increasingly framed as an agentic process that iteratively localizes task-critical moments before perception and reasoning. Moment localization is therefore a key bottleneck: under long-video context constraints, sparse sampling can easily miss decisive evidence, while similarity-based retrieval often returns semantically related but task-irrelevant clips. We present EviScan, an evidence-seeking moment localization model built on an MLLM, designed for task-oriented localization and near-second temporal scanning on hour-long videos. To learn task-oriented localization, we construct ToMo-Pile, a training set that pairs temporal intervals with rationale traces explaining why the interval resolves the task. To make near-second scanning feasible on long videos, EviScan uses DualKV Prefill for memory-efficient streaming inference, and Progressive Localization to first narrow down candidate intervals and then refine boundaries using high-resolution evidence. We further introduce ToMo-Bench, a benchmark for task-oriented moment localization across diverse long-video scenarios. EviScan consistently outperforms specialized localizers and general-purpose MLLMs on both ToMo-Bench and standard temporal grounding benchmarks. When used as a plug-in localization module, it yields substantial gains on downstream long-video understanding benchmarks (MLVU and LongVideoBench), and these gains are larger than those brought by other moment-localization methods. We will release the model, dataset, benchmark, and code.