We investigate whether open-source LLMs encode a linearly separable truthfulness signal in their hidden states, and at which network depth this signal is strongest. Across three $7$B--$8$B instruction-tuned models (Llama-3.1-8B, Mistral-7B, Qwen2.5-7B) loaded in $4$-bit NF4 quantization, we extract per-layer hidden states on four hallucination benchmarks (TruthfulQA, HaluEval-QA, FEVER, and a controlled synthetic set) and compare four detection approaches: linear and MLP probes, INSIDE EigenScore, self-consistency, and attention entropy. A linear probe on a single mid-network layer achieves $0.904$--$1.000$ AUROC on held-out splits, while sampling-based detectors do not exceed $0.541$ AUROC under the same protocol. The truthfulness signal is approximately linear: MLP probes rarely surpass linear probes by more than $0.01$ AUROC. Peak probing layers fall in a consistent band across model families on natural-language benchmarks -- blocks~$13$--$18$ of~$32$ for Llama and Mistral, and blocks~$19$--$25$ of~$28$ for Qwen. First-block attention entropy provides a complementary signal in knowledge-grounded settings ($0.866$--$0.941$ AUROC on HaluEval-QA) at no additional inference cost. The low discriminability of sampling methods under this protocol reflects a structural mismatch between paired-label evaluation and the information these methods access, rather than an inherent limitation of those methods. Code and data are released for full reproducibility on a single $8$\,GB GPU.