Audio deepfake detection (ADD) models are critical for countering the malicious use of text-to-speech (TTS) models. Evaluating and strengthening ADD models requires developing datasets that span the space of generated audio and highlight high-error regions. Existing dataset development strategies face two challenges: (i) manual collection, and (ii) inefficient discovery of blind spots in the ADD models. To address these challenges, we propose FoeGlass, the first black-box automated red-teaming method for ADDs, which effectively discovers ADD failure modes in the space of generated audio underexplored by state-of-the-art deepfake benchmarks. FoeGlass uses the in-context learning capabilities of an LLM to explore the input space of a TTS model, generating audio samples that fool the target ADD using only black-box access to all components. By using a carefully designed context based on diversity measurements, FoeGlass mitigates the common problem of mode collapse in automated red-teaming systems. Empirical evaluations on several open-source ADD and TTS models demonstrate that data generated from FoeGlass substantially improves the false negative rates over unconditional sampling baselines and recent spoofing datasets by up to 94%, while requiring no manual supervision. Furthermore, we show that the attacks generated by FoeGlass are transferable across different target ADDs, demonstrating its broad applicability and ease of use for the automated red teaming of ADD systems. Finally, fine-tuning ADD models on FoeGlass-generated samples notably enhances the robustness of the detectors (up 41%).