Large Language Models (LLMs) have demonstrated remarkable performance across various natural language processing tasks. However, adapting them to domain-specific problems like text-to-SQL generation remains computationally expensive, particularly in dynamic environments where schemas frequently evolve. Full fine-tuning for each new database schema is impractical due to high computational and memory costs. To address this challenge, we propose TraceTune, a parameter-efficient adaptation method that selectively fine-tunes the most relevant attention heads and bias terms identified through causal tracing. Experiments on multiple Text-to-SQL benchmarks demonstrate that TraceTune achieves comparable accuracy to full fine-tuning while significantly reducing memory and compute overhead. These results highlight TraceTune as an efficient and scalable solution for deploying Text-to-SQL systems in resource-constrained environments.