This word appeared in the form tengwiesto “of your reading” in the sentence nai laurë lantuva parmastanna lúmissen tengwiesto “may (a) golden light fall on your book at the times of your reading” (VT49/47). On the same page, Tolkien gives its etymology as the gerund (verbal noun) of the verb tengwa- “to read written matter” (VT49/48). Other attested words for “reading” include cenda or hentië (both based on sight).
Elsewhere this word appears as an element in the word mátengwië “sign language, (lit.) language of the hands”, along with má “hand” (VT47/23). In this word, tengwië could be have the same meaning as above (“sign language” = “✱hand reading”). Alternately, it could be an abstract noun derived from tengwë “sign, token” combined with the abstract-noun suffix -ië, in which case a more literal meaning might be “✱signing” as in “✱the production of signs”. This hypothetical derivation fits nicely with its use in the Quenya word for sign language. More ordinary words for “language” include lambë “a (spoken) language” (LotR/1123, WJ/394) and tengwestië “language (as a concept)” (WJ/394).
#tengwië noun "language" in the compound mátengwië "language of the hands" (VT47:9). Compare tengwë, tengwesta.