This tune is also known by several variations of the name I used, such as Shove That Pig’s Foot Further In The Fire, Shove The Pig’s Foot, Shove The Pig’s Foot A Little Bit Farther Into The Fire, Shove The Pig’s Foot A Little Bit Further Into The Fire, Shove The Pig’s Foot A Little Farther In The Fire, Shove The Pig’s Foot A Little Farther Into The Fire, Shove The Pig’s Foot A Little Further Into The Fire, Shove The Pig’s Foot A Little Nearer To The Fire. It is also known as Ruby With the Dancing Eyes. (http://www.mikekeyes.com)

This is the version we use in our local jam group, but there are quite a few variations to be found in fiddle tune books. I also found lots of videos on YouTube with slight variations of the tune. However, I have not found any twin fiddle sheet music for the tune, though a number of the videos had the fiddlers playing in harmony.

There are two variations of the meaning of the title. One is that “Pig’s Foot” refers either to a blacksmith’s tool for putting a bit of pig iron into the smithy’s fire, or refers to the actual piece of pig iron, which used to be poured out into a mold that resembled piglets suckling at the sow.

The second refers to an old slave story about a slave who stole some pork from his master and hid it under the sheets of his bed. He was telling his wife about his deed when the master came by with a friend and requested that the slave play a tune on his fiddle. The slave obliged playing and singing a tune made up on the spot. The words were:

“Shove that pig’s foot further in the bed
Further in the bed
Further in the bed
Shove that pig’s foot further in the bed
Katie, Katie, Katie, can’t you hear me now”

So, his wife Katie surreptitiously obliged. (https://clawhammerbanjo.net/clawhammer-tune-of-the-week-shove-that-pigs-foot-a-little-further-into-the-fire/)
Somehow the word “bed” got changed to “fire.” But the whole issue is speculative, so choose the explanation you like best.