A noun for “thatch” in The Etymologies of the 1930s derived from primitive ᴹ✶tupsē under the root ᴹ√TUP (Ety/TUP). Its derivation is rather mysterious unless you realize that final -se became -sa in (Old) Noldorin, for example ᴹ✶peltakse > ON. pelthaksa (Ety/PEL). Given this, primitive *tupsā became ON. tuphsa [tuɸsa], when then underwent a-affection to tophsa [toɸsa]. The spirantal ph vocalized to u, and in the resulting tous(a) the diphthong ou became au, producing taus.

Neo-Sindarin: Most of these phonetic changes remain valid in later Sindarin, but it is possible that the combination ps became ff rather than us to produce S. *toph. Nevertheless, I would assume some variations in the ancient Sindarin dialects of Beleriand, and would retain [N.] taus “thatch” as the result in one of those dialects for purposes of Neo-Sindarin.