As large language models (LLMs) increasingly act as collaborative partners, human--AI alignment is often evaluated through explicit task success, accuracy, or reward optimization. Yet many collaborative settings depend on tacit understanding: whether an agent can align with a human's evaluative stance or representational priors without clear objectives, communication, or feedback. To study this capacity, we develop a spectrum-placement task inspired by the social party game Wavelength, in which humans and agents independently place concepts along subjective spectra. We operationalize the Tacit Understanding Index (TUX) as a pairwise measure of similarity between human and agent judgments, and evaluate it with 241 human participants and 200 profile-conditioned LLM agents across four models. We find that nearest human--agent pairs in trait space achieve significantly higher TUX, suggesting that tacit alignment is structured by person-level characteristics rather than random similarity. Regression analyses show that TUX becomes more explainable as predictor sets become richer, with individual traits, decision-making styles, and confidence improving over aggregate trait-distance baselines. These findings suggest that tacit understanding between humans and LLMs is measurable, while revealing the limits of profile-based conditioning for capturing deeper representational alignment.