Gifford’s gloss here is tersely specific and matter-of-fact:
taittering - English dialect: "tilting, seesawing".
The problem here, as so often with Gifford, is that he offers his readers no way of verifying a word that cannot be found in any of the standard dictionaries or reference books, such as the OED, the EDD (English Dialect Dictionary), or any of the smaller specialised glossaries of dialect or slang. Joyce’s extant notes do not offer us much help either. The word was directly transferred from the set of entries under the heading ‘Penelope’ in notebook NLI MS 36,639/4, p. 12r, in the National Library of Ireland. Here we find the phrase “taittering of the lips” struck through in red. But this notebook is a second-order one, made up of random selections from source-ordered notes, arranged according to Ulysses chapter headings. The resulting lack of source context makes the contents harder to identify; however, in this case, we can be almost certain that Joyce took the phrase from pages 163-4 of volume V of Havelock Ellis’s Studies in the Psychology of Sex, subtitled Erotic Symbolism; The Mechanism of Detumescence; The Psychic State in Pregnancy, where we read:
Even in the absence of sexual excitement there is a vague affection, occurring in both married and unmarried women, and not, it would seem, necessarily hysterical, characterized by quivering or twitching of the vulva; I am told that this is popularly termed "flackering of the shape" in Yorkshire and "taittering of the lips" in Ireland.1
This still leaves us with a few questions. Should we now take it as a foregone conclusion that ‘my lips’ in ‘Penelope’ should be reread (and re-translated) as ‘my labia’? Does this re-reading throw out of focus an otherwise touching scene? Or should it be read as another example of Molly’s unsentimental carnality? Could the author have been indulging in a private joke, at the expense of Molly and/or his readers?
Although we now know where Joyce found “taittering”, the word itself still remains something of a lexical mystery, as Ellis offers his readers no documentary information about his allegedly Irish sources here. So in one sense the problem has merely been deferred. It seems very unlikely that the word derives from the Irish language. It bears a tantalizing resemblance to a number of English dialect words, such as ‘titter’ and ‘twitter’, both of which can mean ‘to tremble’, but no evidence exists of ‘taitter’ as a variant, so any connection must remain speculative. So far it looks as though Joyce has snapped up an English hapax posing as a Hibernicism.