I did a little looking using Google's advanced book search facility
and found a reference to "taw" meaning a square dance partner from
1896. The book is _An Illustrated History of Monroe County, Iowa:
..._ [lengthy subtitles omitted], by Frank Hickenlooper. Here's
the relevant passage, from page 214:
At the common "hoedown" those French terms used
by the man who "calls off" are Anglicised into plain English;
for instance, the caller will shout the familiar term "Chassez
partners!" but in the "hoedown" whirl it is translated into:
"Swing your taw,
Everybody dance to please Grandpa!"
I don't see anything in the surrounding text that sheds more light
on the etymology of this usage of "taw". While the passage includes
the word "Chassez", it doesn't include the word "autour". (It
also
seems to imply that the French "Chassez" is equivalent to the English
"swing"--whatever "swing" meant in that part of Iowa at the time
under
discussion--but I wouldn't put any stock at all in that without other,
and stronger, evidence.)
Note: Since Google Books makes scanned images of this entire book
available, I was able to check that the word "taw" found by my search
is indeed what appeared in the text (and not the result of an OCR
error) and that 1896 is indeed the publication date of the book (and
not an OCR error for "1996" or a street address misinterpreted as a
date). I mention this because sometimes when a book search returns
what seems to be an unusually early hit, it's actually the result of
some such error, and they don't always make enough of the book
available to let you check.
--Jim