Multimodal large language models in long chain-of-thought reasoning often fail when different knowledge sources provide conflicting signals. We formalize these failures under a unified notion of knowledge conflict, distinguishing input-level objective conflict from process-level effective conflict. Through probing internal representations, we reveal that: **(I) Linear Separability**: different conflict types are explicitly encoded as linearly separable features rather than entangled; **(II) Depth Localization**: conflict signals concentrate in mid-to-late layers, indicating a distinct processing stage for conflict encoding; **(III) Hierarchical Consistency**: aggregating noisy token-level signals along trajectories robustly recovers input-level conflict types; and **(IV) Directional Asymmetry**: reinforcing the model’s implicit source preference under conflict is far easier than enforcing the opposite source. Our findings provide a mechanism-level view of multimodal reasoning under knowledge conflict and enable principled diagnosis and control of long-CoT failures. Code is available at [anonymous link](https://anonymous.4open.science/r/Diagnosing-Knowledge-Conflict-C78D/).