Here's some information: "High Geared Mama" was written by Jimmie Davis, the "Singing Governor" of Louisiana who also wrote "You Are My Sunshine." (The link gives some interesting biographical information about him.)

The 5-CD set "Nobody's Darlin' But Mine: 1928-1937" (issued by Bear Family in 1998) contains Davis' recordings of both "High Geared Mama" and "High Geared Daddy," which was written by Buddy Jones. Jones performed with Davis and they co-wrote several songs. I suspect one of these songs was an "answer" to the other, but I don't know which came first.

The bio (linked-to above) says that "High Geared Mama" was regarded as a "racy" recording, and Earl Long tried to use it to discredit Davis in a political campaign, but the attempt backfired.

It seems this song would be a good addition to DigiTrad, so I hope someone finds it and posts it here.