We provide causal mechanistic validation that in-context learning (ICL) decomposes into two separable mechanisms: Task Schema (abstract task type recognition) and Binding (specific input-output associations). Through activation patching experiments across 9 models from 7 Transformer families plus Mamba (370M-13B parameters), we establish three key findings: 1. Double dissociation: Task Schema transfers at 100% via late MLP patching; Binding transfers at 62% via residual stream patching -- proving separable mechanisms 2. Prior-Schema trade-off: Schema reliance inversely correlates with prior knowledge (Spearman rho = -0.596, p < 0.001, N=28 task-model pairs) 3. Architecture generality: The mechanism operates across all tested architectures including the non-Transformer Mamba These findings offer a mechanistic account of the ICL puzzle that contrasts with prior views treating ICL as a monolithic mechanism (whether retrieval-based, gradient descent-like, or purely Bayesian). By establishing that Schema and Binding are neurally dissociable -- not merely behavioral modes -- we provide causal evidence for dual-process theories of ICL. Models rely on Task Schema when prior knowledge is absent, but prior knowledge interferes through attentional mis-routing (72.7% recency bias) rather than direct output competition (0%). This explains why arbitrary mappings succeed (zero prior leads to full Schema reliance) while factual overrides fail -- and reveals that the true bottleneck is attentional, not output-level. Practical implications: Understanding these dual mechanisms enables more efficient prompt engineering -- reliable schema transfer reduces required demonstrations for novel tasks, while prior-aware design can mitigate the 38% binding failure rate in high-prior scenarios, improving ICL system reliability in production deployments.