Web-based test automation heavily relies on accurately finding web elements. Traditional methods compare attributes but don't grasp the context and meaning of elements and words. The emergence of Large Language Models (LLMs) like GPT-4, which can show human-like reasoning abilities on some tasks, offers new opportunities for software engineering and web element localization. This paper introduces and evaluates VON Similo LLM, an enhanced web element localization approach. Using an LLM, it selects the most likely web element from the top-ranked ones identified by the existing VON Similo method, ideally aiming to get closer to human-like selection accuracy. An experimental study was conducted using 804 web element pairs from 48 real-world web applications. We measured the number of correctly identified elements as well as the execution times, comparing the effectiveness and efficiency of VON Similo LLM against the baseline algorithm. In addition, motivations from the LLM were recorded and analyzed for all instances where the original approach failed to find the right web element. VON Similo LLM demonstrated improved performance, reducing failed localizations from 70 to 39 (out of 804), a 44 percent reduction. Despite its slower execution time and additional costs of using the GPT-4 model, the LLMs human-like reasoning showed promise in enhancing web element localization. LLM technology can enhance web element identification in GUI test automation, reducing false positives and potentially lowering maintenance costs. However, further research is necessary to fully understand LLMs capabilities, limitations, and practical use in GUI testing.