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."