Equilibrium climate sensitivity is a long-time response property, whereas historical climate records provide only finite, forced projections of the Earth system. This mismatch is important in a complex climate system where slow adjustment, ocean heat uptake, cloud feedbacks, and pattern effects can separate short-term surface-temperature variability from long-term response. We revisit fluctuation-based constraints on climate sensitivity by treating historical temperature variability as a projected fluctuation-memory coordinate. In CMIP5 this coordinate captures a substantial part of the ECS spread, but in CMIP6 the relationship weakens. We show that the missing information is not simply lost: after conditioning on the fluctuation-memory coordinate, CMIP6 retains a strong residual alignment between ECS and a finite CO2-response coordinate estimated from historical forced dynamics. A minimal two-mode stochastic response model, representing surface temperature coupled to a slow hidden response mode, explains this behavior as a hidden response pathway that is weakly projected onto historical fluctuations but visible in finite forced response. These hidden response pathways may involve ocean-mediated adjustment and heat uptake. Linear ARX and Neural ODE response estimators give consistent finite-response coordinates, suggesting that the signal is not an artifact of one dynamical estimator. The results suggest that emergent constraints should be viewed as projected fluctuation-response closure tests in a forced, complex Earth system.