I have only seen one image of Mark Twain playing a guitar. It is a
black and white illustration from the _St. Nicholas_ magazine January
1916 which featured the series titled "The Boys Life of Mark Twain" by
Albert B. Paine. The illustration is by E. F. Ward. The text of the
article does not say that Twain played the guitar. But that is how
illustrator Ward chose to depict the passage which relates to the time
Clemens lived in Keokuk, Iowa and joined the class of a music teacher
who lived in the same building. That illustration is online at:

http://www.twainquotes.com/Music.html

Several years ago guitar collector Hank Risan attempted to prove he
owned Mark Twain's guitar. I do not believe he ever recovered any
convincing evidence.  Risan's attempts have been written about before.
One such article is online at:

http://emol.org/books/twain/

Barb