In 1985, a collection of Muppet comic strips were released in a book titled "
Chickens are People, Too!...But what are Gonzos?". The
Muppet Babies also tackled the subject with the book
What's a Gonzo?.
In the late 90s, the question was posed in the
Ask Henson.com web column, "What exactly
is Gonzo?" Dave Goelz responded: "Nobody knows except his parents, and they're not talking. It was always one of those taboo subjects around the dinner table."
muppet.wikia.com/wiki/Gonzo
In the Muppet Babies storybook
What's a Gonzo, Baby Gonzo goes on an adventure similar to Lewis Carroll's
Through the Looking Glass, where he eventually meets up with many creatures that look like him, but none of them knows the answer, and he ultimately meets The Great Garbanzo.
The Great Garbanzo shows Gonzo his "Onzometer," a tool which can tie shoelaces, shuffle playing cards, make strawberry milkshakes, and answer questions. Gonzo poses his question of "what am I" to the onzometer. Gonzo describes himself to the machine (which the help of his newfound friends) and gets the answer "you are Gonzo." The Great Garbanzo explains that
"you might not know what you are, but you know who you are."
muppet.wikia.com/wiki/What%27s_a_Gonzo%3F