When the positions of two generic singularities of equally signed topological index coincide, a higher-order singularity with twice the index is created. In general, singularities tend to repel each other when sharing the same topological index, preventing the creation of such higher-order singularities in 3D generic electromagnetic fields. Here, we demonstrate that in 2D random vector waves higher-order polarization singularities—known as polarization vortices—can occur, and we present their spatial correlation. These polarization vortices arise from the overlap of two points of circular polarization (C points) with the same topological index. We observe that polarization vortices of positive index occur more frequently than their negative counterparts, which results in an index-symmetry breaking unprecedented in singular optics. To corroborate our findings, we analyze the spatial correlation of C points in relation to their line classification and link the symmetry breaking to the allowed dipolar and quadrupolar moments of the field at a polarization vortex.