We expand on recent work [1]
demonstrating the existence of a novel
entanglement radius $\xi_0$ characterizing flux tube entanglement entropy (FTE$^2$) in (2+1)D Yang-Mills theory. This physical scale
corresponds to the intrinsic thickness of the flux tube that must be fully severed by an entangling region for color degrees of freedom in the flux tube to contribute non-zero FTE$^2$. We consider here geometries of the entanglement region $V$ on the lattice where the length of the region cross-cutting the flux tube is of the same magnitude as $\xi_0$. Our results further the conclusions of [1] by adding detailed new information on the topological structure of the entanglement radius of color flux tubes.