Is there a writing of Wilhelm Gesenius in which he discusses the vowel pointing of the Tetragrammaton that produces the English transliteration "Yahweh"? Does someone have a URL for it?
He discusses the tetragrammaton at several places in the grammar.1 In §102m he includes the vowel pointing patach-šĕwă-sĕgōl that leads to our English “Yahweh”. That is: יַהְוֶה. Elsewhere throughout the grammar he either uses the unpointed יהוה or the Masoretic יְהוָֹה (šĕwă'-ḥōlem-qāmeṣ; that is, the vowels of אֲדֹנָי ʾădōnāy 2). The relationship between these forms and the nature of qere perpetuum is explained in §17c.
As noted in a comment, Gesenius’ lexicon3 also includes an entry for the tetragrammaton with discussion of the historical vocalization. He lists several possilibilities including pataḥ-ḥaṭef pataḥ-ḥōlem (something like yahăwōh) by analogy with יַעֲקֹב (yaʿăqōb, Jacob), consistent with some ancient Greek writings indicating that the Hebrew God was ΙΑΩ (something like iaō). He also discusses some support for the vowels having been šĕwă'-ḥōlem-qāmeṣ (the Masoretic kĕtîb by way of which comes the Western “Jehovah”) and finally discusses the patach-šĕwă-sĕgōl (יַהְוֶה - yahweh), which is supported by the pointing of certain abbreviations for the divine name.
1. Gesenius-Kautzsch-Cowley, Gesenius' Hebrew Grammar (2nd edn; Clarendon Press, 1910).
2. Almost. Just in case anyone is looking too carefully, though ... the first vowel looks different (simple šĕwă in י׳ rather than ḥăṭep̄ páṯaḥ in ădōnāy), but these are related and the change is virtually required by the consonants.
3. Gesenius’s Hebrew and Chaldee Lexicon to the Old Testament Scriptures. Translated by Samuel Prideaux Tregelles. (Bagster and Sons, 1857).