We demonstrate that the ratio of 1/T1 spin-lattice relaxation rates (SLR) of two different isotopes (here 8Li and 9Li) can be used in order to identify the predominant relaxation mechanism within the β-NMR technique. We studied with both isotopes a Pt foil and two samples of single crystal SrTiO3. In Pt, the ratio of the SLR rates was 6.82(29), which is close to but less than the theoretical limit of ∼7.68 for pure magnetic relaxation. In SrTiO3, the weighted averaged SLR ratio of the two samples was 2.7(3), which is close but larger than the theoretical limit of ∼2.14 expected for pure electric quadrupolar relaxation. This indicates that the primary source of relaxation in SrTiO3 is electric quadrupolar in origin and that magnetic effects have a much smaller importance in this material. The low effective asymmetry of 9Li was the dominant cause of uncertainty of the measurements in this study. We propose a system of tagging the beta-decays in coincidence with the alpha decays that take place in two of the three primary decay channels of 9Li as a way of increasing the effective asymmetry and enhance the signal of 9Li β-NMR.