Wordorigins.org

This term meaning a useless task or wasteful endeavor is of uncertain origin, although it is probably related to the word woggle, a term for a Boy Scout’s neckerchief fastener. Boondoggle also has the meaning of a neckerchief fastener or slide in Boy Scout circles and this is likely the original sense of the word.

Woggle makes its appearance in 1923 among scouts in Britain. From The Scout, 9 June 1923:

Wear a scarf woggle.

Woggle is likely related to toggle, the original meaning of which is a pin used to keep a rope in place on shipboard. This sense of toggle dates to the mid-18th century.