https://www.youtube.com/watch?v=XOebYiuTe6M

I've had the noise in the video happen twice now.

Both times the car has been parked on a slight incline and the only way to reproduce is bounce up and down within the car. Sideways movement doesn't make any noise.
I also think both times the car had been stationary for a few days.

Anyone have any thoughts on what this could be?

 

I have noticed this in other cars before. Probably something to do with gravity binding up the suspension with the ebrake being on.

Im sure someone could explain it a little better.

 

Mine does this too.. but as AE said, I think it's just the e-brake.
Try putting it into gear and let it sit on the gears and try it. it won't make the noise.
Or try pulling the e-brake tighter and it may not make the noise

 

ARB droplinks. They run dry and creak like hell. Get it when taking off or slowly over uneven ground. To test disconnect the links temporarily. (Although could be rusted)

 

Your e-brake needs tightening, the car is inching ahead slightly when you do that.

 

I had a squeak too, turns out it was coming from the door, greasing some stuff up and putting some foam padding to stop the passenger door liner from rattling did the trick.