As LLM-based agents increasingly browse the web on users' behalf, a natural question arises: can websites passively identify which underlying model powers an agent? Doing so would represent a significant security risk, enabling targeted attacks tailored to known model vulnerabilities. Across 14 frontier LLMs and four web environments spanning information retrieval and shopping tasks, we show that an agent's actions and interaction timings, captured via a passive JavaScript tracker, are sufficient to identify the underlying model with up to 96\% F1 within a fixed harness. Although fingerprints are harness-specific, with cross-harness transfer falling to near chance, pooling traces across harnesses recovers model identification at 0.74 to 0.81 Macro-F1. We further show that strong classifiers can be trained from roughly one third of the available traces, and that identification improves steadily as more events are observed. Injecting randomised timing delays between actions substantially degrades classifier performance, but does not provide robust protection: a classifier retrained on delayed traces largely recovers performance. We release our code and a labelled corpus of agent traces at https://github.com/KabakaWilliam/known_actions.

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