While induction is considered a key mechanism for in-context learning in LLMs, understanding its precise circuit decomposition beyond toy models remains elusive. Here, we study the emergence of induction behavior within LLMs by probing their response to weak single-token perturbations of the residual stream. We find that LLMs exhibit a robust, universal regime in which their response remains scale-invariant under changes in perturbation strength, thereby allowing us to quantify the build-up of token correlations throughout the model. By applying our method, we observe signatures of induction behavior within the residual stream of Gemma-2-2B, Llama-3.2-3B, and GPT-2-XL. Across all models, we find that these induction signatures gradually emerge within intermediate layers and identify the relevant model sections composing this behavior. Our results provide insights into the collective interplay of components within LLMs and serve as a benchmark for large-scale circuit analysis.