I feel like you might get better results if you rephrased the questions. The 13th Amendment banned slavery, so people who were clamoring for its return were just being nostalgic.

As far as last notable American advocating for slavery, does that include a Lost Cause narrative? I'm sure you can find examples of Strom Thurmond saying slavery was a good thing while stumping for Jim Crow laws. Southern politicians regularly relied on the mythology of the South when running for office after the war and well into the 1960's. It would also have been a prominent theme of any Lost Cause history, including books like Southern by the Grace of God by Michael Grissom (published 1989) or Jefferson Davis's history of the war. (edited to remove an anecdotal comment)

If the question is, when after the Civil War did the South give up on slavery and the notion of actually bringing it back, then it's a little trickier. At first they just re instituted slavery via a complex series of laws, generally called the black codes. These were thrown out in 1866 by the Republicans and new laws had to be passed. There is a period of experimenting with different labor systems before sharecropping is settled on.

After that point, black people are voting much more in mass, have moved to new locations, formed communities, and generally became a lot more independent. White politicians shifted into racist diatribes and were grappling with bigger issues like the vote and retaking office from Republicans. Slavery was dead and banned, so they shifted into oppressing their voting and political rights to keep them working for low wages.

Source: Eric Foner's Resconstruction, David Blight's Race and Reunion.

As a follow up - was there a legal strategy of prosecuting violations of the 13th after its ratification or was the military presence in the south sufficient to enforce the new law without having to get a court order?