As is my wont and pleasure, I looked up the origin of the word gibberish. Etymonline has the following:

gibberish (n.)
“rapid and inarticulate speech; talk in no known language,” 1550s, imitative of the sound of chatter, probably influenced by jabber. Used early 17c. of the language of rogues and gypsies.

jabber (v.)
“talk rapidly and indistinctly,’ 1650s, spelling variant of Middle English jablen (c. 1400), also javeren, jaberen, chaveren, jawin; probably ultimately echoic. Related: Jabbered; jabbering. The noun, “rapid, unintelligible talk” is 1727, from the verb. Related: Jabberment (Milton).

Two things come to mind. One is how cruel it is to speak of ‘rogues and gypsies’ as though the two are or were thought to be synonymous. Were I a gypsy, I would be offended to my boots. And in truth we are all gypsies displaced from somewhere or other.

The second thing that comes to mind is Jabberwocky by Lewis Carroll. He probably named it because it is a nonsense poem – and probably I am the last person on the planet to get the connection.