I have a 2013 4x4 with the 5.0 and during acceleration I get this weird fast paced ticking type noise under the drivers side dash when accelerating sometimes. This is not the normal 5.0 tick you hear during idle, I also have that, but this is different. I also had this in my 1999 Silverado, which makes me think it may be something common.

It is faint and happens inside/behind the dash around my left knee while driving. Passengers can't notice it and my phone won't pick it up over the engine and tire noise. It is hard to explain but I am sure if anyone else has noticed it will know what I mean. I don't think it is an exhaust leak, it doesn't sound like that. I want to say it almost sounds like a fan or something. It ONLY happens when accelerating, and doesn't always do it. The lower RPM the less noticeable. I don't notice any loose brackets or anything when poking around in the engine bay.

I now realize how vague this is, I will try and get a better description while I hear it in real time here shortly.

 

Is it your HVAC doors? They make noise.

 

I'm not familiar with them but it does kind of sound like something tiny flapping in the wind. It will do it with the air on or off, though.