"Jane, Jane" is on a 1957 album titled American Folk Songs Sung by the Seegers. The voice is clearly Peggy. Notes were by Charles Seeger Sr.

https://folkways-media.si.edu/docs/folkways/artwork/FW02005.pdf

JANE JANE (THREE MOCKINGBIRDS) - a Negro ring game from Mississippi, in which there is one player who steals partners and jumps while the song is sung. Melodically it is akin to "Stewball," with its answer-back chorus and short solo, and is a popular Negro song pattern.

Leader: Hey, he-ey
Group: Jane, Jane
Leader: My Lordy, Lord
Group: Jane, Jane
Leader: I'm gonna buy
Group: Jane, Jane
Leader: Three mockingbirds
Group: Jane, Jane
Leader: One for to whistle
Group: Jane, Jane
Leader: One for to sing
Group: Jane, Jane
Leader: One for to do
Group: Jane, Jane
Leader: Most any little thing

Leader: Hey, he-ey
Group: Jane, Jane
Leader: My Lordy, Lord
Group: Jane, Jane
Leader: I'm gonna buy
Group: Jane, Jane
Leader: Three hunting dogs
Group: Jane, Jane
Leader: One for to run
Group: Jane, Jane
Leader: One for to shout
Group: Jane, Jane
Leader: One to talk to
Group: Jane, Jane
Leader: When I go out

Leader: Hey, he-ey
Group: Jane, Jane
Leader: My Lordy, Lord
Group: Jane, Jane
Leader: I'm gonna buy
Group: Jane, Jane
Leader: Three muley cows
Group: Jane, Jane
Leader: One a-for to milk
Group: Jane, Jane
Leader: One to plough my corn,
Group: Jane, Jane
Leader: One for to pray
Group: Jane, Jane
Leader: On Christmas morn

Leader: Hey, he-ey
Group: Jane, Jane
Leader: My Lordy, Lord
Group: Jane, Jane
Leader: I'm gonna buy
Group: Jane, Jane
Leader: Three little blue birds
Group: Jane, Jane
Leader: One a-for to weep
Group: Jane, Jane
Leader: One for to mourn
Group: Jane, Jane
Leader: One for to grieve
Group: Jane, Jane
Leader: When I am gone
Group: Jane, Jane


And then Peter, Paul and Mary and Tia Blake append "Children Go Where I Send Me."