Phenotypic traits do not always respond to selection independently from each other and often show correlated responses to selection. The structure of a genotype-phenotype map (GP map) determines trait covariation, which involves variation in the degree and strength of the pleiotropic effects of the underlying genes. It is still unclear, and debated, how much of that structure can be deduced from variational properties of quantitative traits that are inferred from their genetic (co)variance matrix (G-matrix). Here we aim to clarify how the extent of pleiotropy and the correlation among the pleiotropic effects of mutations differentially affect the structure of a G-matrix and our ability to detect genetic constraints from its eigen decomposition. We show that the eigenvectors of a G-matrix can be predictive of evolutionary constraints when they map to underlying pleiotropic modules with correlated mutational effects. Without mutational correlation, evolutionary constraints caused by the fitness costs associated with increased pleiotropy are harder to infer from evolutionary metrics based on a G-matrix's geometric properties because uncorrelated pleiotropic effects do not affect traits' genetic correlations. Correlational selection induces much weaker modular partitioning of traits' genetic correlations in absence then in presence of underlying modular pleiotropy. This article is protected by copyright. All rights reserved.