The story
From tiddlywink + -s, possibly from tiddly (“(informal) little, tiny”) + wink (“blinking of one eye”), perhaps borrowed from tiddlywink, etymology 1 (“unlicensed beerhouse or pawnshop; game played using dominoes”, etc.). The game was patented by a British bank clerk, Joseph Assheton Fincher (1863–1900), on 19 October 1889, and the name Tiddledy-Winks trademarked by him the same year. Tiddlywinks is the preferred modern spelling; the earliest known use of this spelling dates from 1894.
Etymology from Wiktionary, CC BY-SA 4.0.