  We demonstrate the application of implanted-ion $\beta$-detected NMR as a
probe of ionic liquid molecular dynamics through the measurement of $^8$Li
spin-lattice relaxation (SLR) and resonance in 1-ethyl-3-methylimidazolium
acetate. The motional narrowing of the resonance, and the local maxima in the
SLR rate, $1/T_1$, imply a sensitivity to sub-nanosecond Li$^+$ solvation
dynamics. From an analysis of $1/T_1$, we extract an activation energy ${E_A =
74.8 \pm 1.5}$ meV and Vogel-Fulcher-Tammann constant ${T_{\mathrm{VFT}} =
165.8 \pm 0.9}$ K, in agreement with the dynamic viscosity of the bulk solvent.
Near the melting point, the lineshape is broad and intense, and the form of the
relaxation is non-exponential, reflective of our sensitivity to heterogeneous
dynamics near the glass transition. The depth resolution of this technique may
later provide a unique means of studying nanoscale phenomena in ionic liquids.
