The “root” ᴹ√TINKŌ (more likely just a primitive word) appeared in The Etymologies of the 1930s with the gloss “metal” and derivatives like ᴹQ. tinko/N. tinc of the same meaning (Ety/TINKŌ). The reappearance of Q. tinco “metal” in The Lord of the Rings appendices (LotR/1122) strongly indicates its ongoing validity.
ᴹ√TINKŌ may have replaced the root ᴱ√SINI “pale blue” from the Qenya Lexicon of the 1910s with derivatives like ᴱQ. sink “mineral, gem, metal” and G. sinc “metal” (QL/83; GL/67); these early mineral words were originally attributed to ᴱ√SṆT͡YṆ “twinkle” before they were transferred to ᴱ√SINI, leaving only derivatives like ᴱQ. sintl “crystal” and ᴱQ. sinty- “sparkle” under ᴱ√SṆT͡YṆ (QL/85). However, in notes from the late 1960s Tolkien had primitive ✶sinki as an element ✶sinkitamo, the basis for Q. sintamo “smith” (PE17/108). Likewise there is evidence of the earlier root in Q. sinca “flint” as in Q. sincahonda “flint-hearted” (LotR/979), initially given as ᴹQ. tingahondo in Lord of the Rings drafts (SD/68).
Neo-Eldarin: For purposes of Neo-Eldarin, I would definitely use ✶tink- = “metal”, but I think it is worth keeping ✶sinki = “✱mineral = any inorganic solid including both stone and metal” as a variant.
A root in The Etymologies of the 1930s, first glossed “copper” and then “metal”, with derivatives ᴹQ. rauta/N. rhaud “metal” and serving mainly to explain names like N. Angrod and N. Finrod (Ety/RAUTĀ). It might have reappeared in the name S. Rodëol “metal of Eöl” from later Silmarillion drafts (WJ/322), but by 1957 Tolkien was explaining the final element of S. Finrod as S. raud “noble” (PE17/49, 118), so I think it is likely that ᴹ√RAUTA “metal” was abandoned.
Neo-Eldarin: For purposes of Neo-Eldarin, I’d use Q. tinco (LotR/1122) and its cognate [N.] tinc (Ety/TINKŌ) for “metal” words. For “copper” I'd use derivatives of √(U)RUS (VT41/10).