We introduce ARGOS, the first benchmark and framework that reformulates multi-camera person search as an interactive reasoning problem requiring an agent to plan, question, and eliminate candidates under information asymmetry. An ARGOS agent receives a vague witness statement and must decide what to ask, when to invoke spatial or temporal tools, and how to interpret ambiguous responses, all within a limited turn budget. Reasoning is grounded in a Spatio-Temporal Topology Graph (STTG) encoding camera connectivity and empirically validated transition times. The benchmark comprises 2,691 tasks across 14 real-world scenarios in three progressive tracks: semantic perception (Who), spatial reasoning (Where), and temporal reasoning (When). Experiments with four LLM backbones show the benchmark is far from solved (best TWS: 0.383 on Track 2, 0.590 on Track 3), and ablations confirm that removing domain-specific tools drops accuracy by up to 49.6 percentage points.