Despite recent progress, Biomedical Entity Linking (BEL) with large language models (LLMs) remains computationally inefficient and challenging to deploy in practical settings. In this work, we demonstrate that instruction-tuning of open-source generative models can offer an effective solution when applied at the re-ranking stage of the BEL pipeline. We propose a set-wise instruction-tuning formulation that enables fast and accurate candidate selection. Our method demonstrates strong performance on multiple BEL benchmarks, yielding significant improvements in linking accuracy (3%-24%) while reducing inference time compared to the state-of-the-art. We integrate our generative re-ranker into BeLink, a modular, end-to-end system designed for practical real-world BEL applications.