We report β−NMR measurements in Bi2Se3:Ca and Bi2Te3:Mn single crystals using 8Li+ implanted to depths on the order of 100 nm. Above ∼200K, spin-lattice relaxation reveals diffusion of 8Li+, with activation energies of ∼0.4eV (∼0.2eV) in Bi2Se3:Ca (Bi2Te3:Mn). At lower temperatures, the NMR properties are those of a heavily doped semiconductor in the metallic limit, with Korringa relaxation and a small, negative, temperature-dependent Knight shift in Bi2Se3:Ca. From this, we make a detailed comparison with the isostructural tetradymite Bi2Te2Se [McFadden et al., Phys. Rev. B 99, 125201 (2019)]. In the magnetic Bi2Te3:Mn, the effects of the dilute Mn moments predominate, but remarkably the 8Li+ signal is not wiped out through the magnetic transition at 13 K, with a prominent critical peak in the spin-lattice relaxation that is suppressed in a high applied field. This detailed characterization of the 8Li+ NMR response is an important step toward using depth-resolved β−NMR to study the low-energy properties of the chiral topological surface state in the Bi2Ch3 tetradymite topological insulator.