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1.
A semi-erect penis. Usually 1/2 to 3/5 the way to being fully erect.

Also can be simplified to "Gonzo".

Variations of term:

Gonzor: The one who is causing the Gonzo Nose. Usually female.

Gonzee: The one who is getting the Gonzo Nose. Male.

Upside-Down Gonzo Nose - An overly erect penis.

Gonzette: Female who habitually causes Gonzo Noses.

For clarification, see image of the character "Gonzo" from Jim Henson's "The Muppets".
Gonzor - "Hey, you ready to bang me?"

Gonzee - "Nope, all I got is a Gonzo Nose."

Gonzor - "Well, you need to hurry and turn that Gonzo in to an Upside-Down Gonzo Nose so you can jam it in my a-hole."

Gonzee - "Okay."
by Banghorse July 28, 2009
 
2.
When positioning oneself with the ass on the forehead of one's sex partner, one slaps his penis down on the partner's nose, resembling the long, extruding nose of Gonzo from the Muppets. Typically performed while giving the Arabian Goggles.
While Eric was screwing that chick, he decided to pull out and give her the Arabian Goggles, and for emphasis he slapped on the Gonzo Nose!
by xer0negative November 29, 2007
 
3.
Some one who has a large protruding nose that curves down
Jason shut up or I'll hit you in your Gonzo nose
by Alex Lopz November 27, 2006
 
4.
A boner that curves a little at the end.
"You hoes can pogo on my gonzo nose."
by pedro romero June 08, 2005