Here's something I'm keen to share with you - that "twitter" was 1950s slang for menstruation.
My source is the 1957 novel Fowlers End, by Gerald Kersh. On page 210 of my edition (Valancourt Books, 2013) the narrator, Dan Laverack, has the following exchange with his girlfriend, June. She explains to him that she is not, as previously thought, pregnant. Dan asks her how she can be so sure:
"I'm trying to make you understand it was the little birdies that go tweet-tweet-tweet," she said.
"This I do not understand."
"Well, if you want me to put it in plain English, I was squiffy, and twittered." And when I still failed to grasp her meaning, she said, "Wait a minute," and got out What Every Girl Should Know, turned the pages until she found the item she wanted, which she marked for me with a delicate pink thumbnail. Feminine euphemisms never fail to amuse and astonish me; women will employ the vilest vulgarisms and the most sickeningly elusive argot rather than the clear scientific term. June Whistler was simply menstruating.
I can find no other evidence that twitter/twittering carried such a meaning (although Kersh employs the term several times on subsequent pages, at one point having Dan call June, affectionately, a 'twitterer').