The Sindarin dual was almost certainly derived from the same primitive form ✶ata as the Quenya dual ending -t, indicating this ending was ancient in form. The other Quenya dual, -u, would not have been active in Sindarin since final vowels were lost.
Tolkien stated (Let/427) that this ending was archaic and lost, but did not state when it disappeared. The ending may have still been active in the First Age. The ending appears in the day-name Orgaladhad “Day of the Two Trees”. Since the Sindar had no direct experience with the trees, this word was likely adopted from its Quenya cognate Aldúya when the Noldor and Sindar were reunited.
A primitive “dual” element mentioned in notes on numbers from the late 1960s, contributing to the forms of primitive ✶enekwe “six” and ✶yun(e)kwe “twelve” in the Quenya branch of Elvish, as well as the ancient 1st person inclusive pronoun ✶ñwe (VT48/10). It was probably related to the ancient dual suffix ✶-ū (Let/427). It was also likely a later iteration the dual root ᴱ√WI from the Qenya Lexicon of the 1910s which was likewise connected to dual U (QL/33). This early root was mentioned in the contemporaneous Gnomish Lexicon as ᴱ✶u̯i (GL/45).