Fault localization (FL) aims to identify buggy program elements that are responsible for observed failures. To reduce the time and effort developers spend on debugging, numerous automated FL techniques have been proposed. Statisticbased FL (STBFL) techniques mainly analyze the test coverage information to prioritize potentially faulty elements. While effective, they require many test cases, mutation data, or other auxiliary artifacts, which are often difficult or costly to obtain. Recently, with the rapid advancement of large language models (LLMs), many LLM-based FL techniques have been proposed. LLM-based FL offers high practicality because it requires only a few failing tests as its artifacts, but they rely on commercial LLMs, which raise code security concerns or incur substantial infrastructure costs. In this paper, we present MixFL, a methodlevel FL framework enabled by the combination of language models for code (CodeLMs) that are lightweight and specialized for code-related tasks. MixFL allows multiple CodeLMs to embed the source code and comments of methods covered by failing tests, and employs a gating network to adaptively mix their embeddings before computing suspiciousness scores with a deep neural classifier. Due to its design, MixFL can perform effective FL using lightweight CodeLMs that can be deployed on modest infrastructure. On the Defects4J benchmark, which consists of 395 bugs from six real-world Java projects, we conduct a comprehensive investigation into how different combinations of CodeLMs affect FL performance and derive several meaningful findings. In addition, we show that MixFL can outperform the state-of-the-art STBFL and LLM-based FL approaches.