Large language models (LLMs) are increasingly applied to ranking tasks in retrieval and recommendation. Although reasoning prompting can enhance ranking utility, our preliminary exploration reveals that its benefits are inconsistent and come at a substantial computational cost, suggesting that when to reason is as crucial as how to reason. To address this issue, we propose a reasoning routing framework that employs a lightweight, plug-and-play router head to decide whether to use direct inference (Non-Think) or reasoning (Think) for each instance before generation. The router head relies solely on pre-generation signals: i) compact ranking-aware features (e.g., candidate dispersion) and ii) model-aware difficulty signals derived from a diagnostic checklist reflecting the model's estimated need for reasoning. By leveraging these features before generation, the router outputs a controllable token that determines whether to apply the Think mode. Furthermore, the router can adaptively select its operating policy along the validation Pareto frontier at deployment time, enabling dynamic allocation of computational resources toward instances most likely to benefit from Think under varying system constraints. Experiments on three public ranking datasets with different scales of open-source LLMs show consistent improvements in ranking utility with reduced token consumption (e.g., +6.3% NDCG@10 with –49.5% tokens on MovieLens with Qwen3-4B), demonstrating reasoning routing as a practical solution to the accuracy-efficiency trade-off.