Hyper-Raman spectra of six samples of ${\mathrm{K}}_{1\ensuremath{-}x}{\mathrm{Li}}_{x}{\mathrm{TaO}}_{3}$ with Li concentrations $x$ between 0.008 and 0.087 are measured in the wave number range below $120 {\mathrm{cm}}^{\ensuremath{-}1}$ at temperatures well above the transitions to glassy or ferroelectric-type states. An internal reference method is demonstrated based on a comparison of hyper-Rayleigh and hyper-Raman scattering intensities recorded under identical conditions. With the soft-mode hyper-Raman line being taken as calibration standard, absolute values of the permanent dipole moment and the first-order hyperpolarizability of the polarization clusters around the off-center Li ions are obtained. Although only integrated intensities are involved, our procedure requires a detailed analysis of the spectral broadening of the hyper-Rayleigh line, which exceeds $1 {\mathrm{cm}}^{\ensuremath{-}1}$ above 200 K. This analysis yields evidence that hyper-Rayleigh scattering solely results from thermally activated hopping motions of the Li ions and that orientational correlations between the Li ions may be ignored in the high-temperature limit under study. At room temperature our results are ${p}_{\mathrm{PC}}^{*}=18 \mathrm{D}$ (Debye units) $=^3.7e\mathrm{\AA{}}$ (electron charge times length measured in \AA{}) and ${\ensuremath{\beta}}_{222}=1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30} {\mathrm{g}}^{\ensuremath{-}1/2} {\mathrm{cm}}^{7/2}\mathrm{s}$ (cgs units) $=^4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}40} {\mathrm{m}}^{4}{\mathrm{V}}^{\ensuremath{-}1}$ (SI units), where ${p}_{\mathrm{PC}}^{*}$ and ${\ensuremath{\beta}}_{222}$ are the effective dipole moment of a polarization cluster and the dominant component of its hyperpolarizability tensor, respectively. Both quantities increase with decreasing temperature and reflect the growth of the polarization clusters due to the slowing down of the soft mode. A temperature-independent intrinsic or core dipole moment ${p}_{\mathrm{PC}}=2.3$ $\mathrm{D}=^0.48e\mathrm{\AA{}}$ is deduced from ${p}_{\mathrm{PC}}^{*}$ and discussed with regard to the off-center displacement of the Li ion.