gås is from Proto-Indo-European *ǵʰans- "goose", as in English goose, Latin ānser, Greek χήν. The Old High German word was gans, and the AHD tells us that this word or a closely related word was borrowed into Spanish as ganso "goose, fool". The OED tells us that this is a possible source of gonzo. It could also be from Italian gonzo "foolish"; I don't know if this is related to the Spanish word.
This quote from the OED gives some clues to gonzo's origin:
1972 in R. Pollack Stop Presses (1975) 184, I ask Hunter to explain... Just what is Gonzo Journalism?.. ‘Gonzo all started with Bill Cardosa,..after I wrote the Kentucky Derby piece for Scanlan's..the first time I realized you could write different. And..I got this note from Cardosa saying, ‘That was pure Gonzo journalism!’.. Some Boston word for weird, bizarre.’