Among the family of non-overlapping domain decomposition methods, the Dual-Primal Finite Element Tearing and Interconnecting method (FETI-DP) of Farhat et al. has gained prominence for its versatility, robustness, and scalability. However, in problems with high contrast in material properties—particularly when discontinuities align with subdomain interfaces—its performance can degrade significantly. While scaling techniques such as rho- and Deluxe-scaling help alleviate these issues, they are not always sufficient. To restore robustness, the coarse space often requires enrichment beyond the standard set of primal degrees of freedom (typically subdomain corners). Early enrichments, such as interface averages, higher-order moments, or coefficient-weighted constraints, offered improvements but lacked generality. A more systematic strategy was introduced by the adaptive coarse spaces pioneered by Mandel and Sousedík, which identify problematic interface modes via local generalized eigenvalue problems (GEVPs). While offering provable robustness, solving a GEVP for each interface is computationally intensive, and in many cases, the cost outweighs the benefit. Nonetheless, these adaptive approaches offer critical insight into what constitutes an effective coarse space. Building on this and heuristics such as Frugal FETI-DP, we propose a strategy that exploits coefficient distributions along interfaces to construct a reduced basis for the GEVPs used in adaptive coarse space construction. Through numerical examples—from academic binary distributions to problems in modular topology optimization—we show that RB-GEVP achieves near-equivalent mode detection using GEVPs that are orders of magnitude smaller. The resulting condition numbers remain comparable to those obtained by full adaptivity, but at a fraction of the computational cost.