The "sweet potato" is another name for the ocarina, a small instrument played by mouth. According to Wiki:

The ocarina ( /ɒkəˈri¢°nə/) is an ancient flute-like wind instrument.[1] While variations exist, a typical ocarina is an oval-shaped enclosed space with four to twelve finger holes and a mouthpiece that projects from the body. It is often ceramic, but other materials, such as plastic, wood, glass, and metal may also be used.

In the 1941 movie "Meet John Doe," Gary Cooper and Walter Brennan play duets on harmonica and ocarina. Cooper was a fairly serious harmonica player and took every opportunity to play it in his films.