In order to resolve two previous conflicting reports on detectable but weak nuclear magnetic resonance (NMR) 33S signals in unenriched EuS, a sample of 33S-enriched EuS was prepared and the NMR and its temperature dependence were measured in the range from 1.3 to 4.2 K. It was verified that the T=0 extrapolated NMR signal has a value of 12.73 MHz (≈ 39 kG), not 5.4 MHz, as one group had reported. The temperature dependence of the NMR was used to assess the applicability of two proposed spin-wave-region power-law schemes. The schemes attempted to systematize and explain the simple power-law behaviors measured by NMR and other techniques that have been reported (or have been present in measured data, but not reported) for more than five decades. The scheme proposed by Koebler et al. [Physica B 364, 55 (2005)] contends that the low-temperature magnetization of EuS follows a simple T2 behavior all the way up to 0.75Tc. The 33S spin-echo measurements are consistent with a power law, but cast doubt on the T2 dependence. Possible reasons for discrepancies between various EuS NMR measurements are discussed in the paper as well as means of resolving such issues by future experiments.