  We report measurements on the high temperature ionic and low temperature
electronic properties of the 3D topological insulator Bi$_2$Te$_2$Se using
ion-implanted $^8$Li $\beta$-detected nuclear magnetic relaxation and
resonance. With implantation energies in the range 5-28 keV, the probes
penetrate beyond the expected range of the topological surface state, but are
still within 250 nm of the surface. At temperatures above ~150 K, spin-lattice
relaxation measurements reveal isolated $^8$Li$^{+}$ diffusion with an
activation energy $E_{A} = 0.185(8)$ eV and attempt frequency $\tau_{0}^{-1} =
8(3) \times 10^{11}$ s$^{-1}$ for atomic site-to-site hopping. At lower
temperature, we find a linear Korringa-like relaxation mechanism with a field
dependent slope and intercept, which is accompanied by an anomalous field
dependence to the resonance shift. We suggest that these may be related to a
strong contribution from orbital currents or the magnetic freezeout of charge
carriers in this heavily compensated semiconductor, but that conventional
theories are unable to account for the extent of the field dependence.
Conventional NMR of the stable host nuclei may help elucidate their origin.
