It L Go, Thanks! The sound described below is exactly the sound I hear..Saved me from uselessly changing the oil (today!) before a sump exchange...I can print this out and go to the dealer and save everyone a lot of time..Below is the first post from corvette forum then his followup. I will post a followup myself to confirm this was the sound and how they fix it.
from:
Brand New Z06 - Help!! - Corvette Forum
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I took museum delivery on the 14th of my 2008 Z06. Absolutely love the car, but after 700 happy miles, I think I have a problem. About 50 miles ago the car started developing a popping noise that appeared to be coming from behind or underneath the dash on the passenger side. It’s most pronounced around 1800-2200 rpm. It kind of sounds like popcorn in the microwave, but not as loud.
I’ve spent the past two days driving myself crazy trying to find the cause of the sound. It’s too loud to be a relay and it’s definitely not coming from the fuse panel. I’ve listened everywhere inside the car. I’ve even used a stethoscope. I think the noise must be coming from outside underneath the car and yet I can’t even hear it with the hood open and my ear to the engine bay.
My best guess is it’s coming from the exhaust system – Specifically, the catalytic converter /s and the design of the car amplifies the sound and makes it appear as though the sound is coming from underneath or behind the dash.
I know. . . It seems like a stretch, but it sounds very similar to the noise the exhaust system and catalytic converters make when you turn the car off (popping and clicking sound) as the exhaust cools.
I’ve filled up twice at different stations and the sound is still there, so I’ve ruled out bad fuel.
It’s definitely not the drive train or differential because the sound is still present when the clutch is depressed and/or the car is not moving.
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Sorry took so long to get back to you guys – Well… the dealer did a hell of a job finally isolating the noise. It turned out to be the oil tank (Z06 dry sump system). There's a small tubular screen at the bottom of the tank that came loose and was rattling/vibrating in the tank.
Now that's one for the books! - Couldn't find anyone else with a similar problem. I have heard a few complaints of noise behind the passenger side dash and the dealer telling the individual it's just a relay. If the noise is pronounced (louder than a typical relay) and the car is a Z06, I suggest you check the oil tank.
It's incredible how difficult it can be to isolate a noise - Even with a stethoscope it took the dealer several hours to find it - No BS, I was there watching!
Most importantly, it was the best dealer experience (dealer name OMITTED) I've ever had! I didn't even buy the car from them and they treated me like a lifelong customer.
I recently retired from the Army and settled in Decatur, AL. I have to say there's something to be said for how people treat you in a small town.
It was a very easy job (swap tanks) and I got that 1000 mile oil/filter change out of the way 
