Your going to need a new belt aswell, Bando brand is actually OEM toyota

 

Going to bump this thread up a bit. I am / was(?!) having this problem. I too, thought okay drive belt or pulley on an accessory or the idler... it would happen when accelerating/decelerating or just blipping the throttle "quickly" even in park...

With no help though I was unable to rev the engine while sticking my nose into the engine bay and could never pinpoint anything. I checked my belt with a gauge and it seemed fine (and looks fine).

So I did the next best thing and pressed the accelerator with my hand with my head under the car (yeah well that sounds slightly stupid when writing it out). I noticed that when I hit the accelerator the exhaust would jostle... and my eyes brought me to a rusted through retainer ring near the middle of the car. I had previously replaced one further up a couple of years ago just because and I bought a spare (from hardware store...just one of those stainless ring clamps - why are the factory ones iron?!) at that time so I replaced it.

I noticed when I would jostle the rusted ring area it would squeak similarly to the blasted noise I was hearing... after getting the rusted one off and putting a new one on and tightening it up... I couldn't reproduce the noise (at least in the driveway in a few minutes).

Time will tell but hopefully all it was is a rusty ring clamp rubbing against the exhaust/heat shield under there. Car noises are the worst you can never tell where they're coming from... thought I'd write what I found in case it helps you or anybody else stumbling in here in the future - it may be nothing more than a $1/1 minute fix.

Then again, mine wasn't constantly making the noise only somewhat randomly when starting and stopping and not doing it just idling really.