TurnMaster: A Synthetic Spoken Dialogue Benchmark for Voicebot End-Of-Turn detection

End-of-turn (EOT) detection enables real-time voicebots to respond promptly without interrupting within-turn pauses. However, existing resources do not jointly provide scale, task-oriented structure or temporal control required for EOT research. We introduce TurnMaster, a large-scale synthetic spoken-dialogue corpus derived from Taskmaster dialogues. It provides synthesized user speech, reference transcripts, dialogue-level speaker consistency, speaker-disjoint splits, and controllable variants incorporating disfluencies and extended pauses. The corpus is curated through dual-ASR validation and duration-based filtering. We also propose a response-time-conditioned streaming Conformer-Transducer, allowing EOT behavior to be adjusted at inference time. Experiments show that budget-conditioned training improves the latency/cutoff trade-off over fixed-budget models, both on TurnMaster and out-of-domain EOT-Bench evaluation.