This is dance #11180 in The Caller's Box, a contra dance database.
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The Rival
by Ralph Page
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Figures:
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Calling Notes:
The A1 action is described as "Couples 1 & 2 figure eight across the set". It isn't specified who crosses first and who casts. I'm guessing by flow into the A2 that the ones start by going down the outside.
It could also be a hey. In "Ways of the World" (Vol 9 No 3 p 27) , Ralph Page describes the hey as "Figure 8 with the two couples below (on own side)" Likewise for "Calico and Crinoline" (Junket Vol 14, No 3, p 21). But these are heys for three on the sides. This would be four people doing a hey for four across the set, and Ted Sannella claims "Bonnie Jean" was the first hey for four in a modern contra.
Until someone does deep digging into the Ralph Page collection at the Unversity of New Hampshire Library, this will likely remain a mystery.
(Update: See also Stockton Dance Camp Syllabus for 1956, on page 94 , when Ralph Page called the square "Figure Eight", with a figure named "FIgure Eight" that's clearly a hey for four.)