What is the Tumtum tree in Jabberwocky?

The Tumtum tree is the tree by which the boy rested in the poem Jabberwocky, which appeared in the book Through the Looking Glass, the sequel to Alice's Adventures in Wonderland.

He took his vorpal sWord in hand:

Long time the manxome foe he sought --

So rested he by the Tumtum tree,

And stood awhile in thought.

Carroll offered definitions for many of the Words in the poem Jabberwocky, but never described what he meant by Tumtum tree. It is arguable that the nonsense Words don't really have or need proper definitions, and it is the sounds of the Words, the feelings they invoke and the ideas they suggest which is what is important, therefore, all that matters is what 'Tumtum tree' means to you, as a reader.

However, in his Annotated Alice, Martin Gardner says that "Tum-tum was a common colloquialism in Carroll's day, referring to the sound of a stringed instrument, especially when monotonously strummed," so perhaps this is the inspiration behind the term.