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Many agents in real-world environments cannot reliably communicate their goals through language, including household pets, pre-verbal infants, and other non-speaking embodied agents. In such settings, intent must be inferred from incomplete behavioral observations in context-rich environments. This creates a core ambiguity: observable behavior is often noisy or underspecified, while context provides strong prior information but can also induce brittle shortcut predictions if used naively. We present CatSignal, a Bayesian-inspired probabilistic framework for multimodal intent inference that models spatial context as a prior-like constraint and behavioral observations as evidence. Rather than treating context as an ordinary input feature, our method uses a context-gated Product-of-Experts formulation to compute posterior-like intent distributions from context, pose dynamics, and acoustic cues. We instantiate this formulation in a household cat setting as a focused proof-of-concept for intent inference in non-speaking agents. Under Leave-One-Video-Out evaluation on a multimodal domestic cat dataset, the proposed prior-guided fusion achieves the best overall accuracy of 77.72%, outperforming feature concatenation (71.83%) and stronger late-fusion baselines. More importantly, it substantially reduces context-driven shortcut failures in ambiguous cases. While simpler fusion strategies remain competitive in Macro-F1 and selective prediction, the proposed model provides the strongest overall accuracy and the best suppression of context-based shortcut collapse.