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Howard Stern show, the Whack Pack, remember that when they did the "Wazz up" commercial with High Pitch, Crackhead Bob, Beatlejuice, Stuttering John???
Things like that can drive you nuts. Assuming it isn't a bird in the hatch, and risking the comments that may follow this suggestion, put someone small in the back and have them listen while you drive around the block.
When I have my music off I can hear an intermiten kind of chirping sound as well. Its not too loud, but its still there. What year is your Z? Mine is a 2005.
Bet you it's the Z emblem cover on your shock tower bar. It's been a known issue on a lot of cars, really high pitched sound too. My 06 has it too, but only if I touch it, like when I'm cleaning it. It hasn't yet made the sound while I'm driving so it doesn't bother me yet.