Large language models (LLMs) are increasingly used in information retrieval (IR) pipelines as relevance judges and re-rankers. Yet most analyses remain output-centric, evaluating generated labels or scores while offering limited insight into how relevance is represented inside the model. In this work, we study whether query-document ($q$-$d$) relevance is linearly decodable from residual-stream activations in instruction-tuned LLMs, how this internal signal compares with generated relevance judgments, and whether it transfers across languages. Using the TREC DL20 and MIRACL test collections, we guide medium-scale LLMs (4-9B parameters) with UMBRELA-style relevance judgment prompts, extract last-token activations from every transformer layer, and train linear probes to predict relevance labels. We compare probe predictions with generated judgments and use TREC DL20 to test whether probe-derived pseudo-labels preserve system rankings when compared with human judgments. Our results suggest that $q$-$d$ relevance is encoded as a depth-dependent internal signal: probe performance is weak in early layers and strongest in middle-to-late layers, indicating that relevance becomes more linearly accessible after contextual integration. Most importantly, in several models, validation-selected probes match or outperform generated judgments and better preserve system rankings, revealing a separation between internal relevance representation and external expression. Multilingual experiments further suggest partial cross-language portability, although transfer remains weaker than within-language decoding. Overall, this work provides a representation-level perspective on LLM-based relevance assessment. Layer-wise probing can help diagnose where relevance emerges, when generated judgments fail to reflect internally available evidence, and how relevance representations vary across languages, datasets, and model families.