Can light localize in any three-dimensional disordered dielectric?

Vector electromagnetic waves in a 3D disordered, non-absorbing dielectric (index contrast $n$, filling fraction $f$, scatterer size $a$ relative to wavelength $\lambda$, structural correlations). Point-dipole ensembles show no localization at any density because of the longitudinal $1/r^3$ near-field coupling (Skipetrov and Sokolov, PRL 2014), and FDTD simulations of random dielectric sphere packings show none up to $n = 10$. Question: does any dielectric structure (correlated or hyperuniform networks near a photonic band edge, impurities in a solid matrix, high-index nonspherical particles) have a mobility edge, and can an experiment show it with signatures not mimicked by absorption or fluorescence (scale-dependent diffusion $D(L)$, normalized transmission fluctuations $\operatorname{var}(s_{ab}) > 7/3$, Thouless number $g < 1$).

Time- and size-resolved transmission measurements on an absorption-free 3D dielectric sample showing $D(L)$ decreasing to zero and $g < 1$, matched by full-wave simulations of the same structure.