Can't get z-index to work for div inside of another div

A positioned container always contains its children. You can't have the content of a container below the container itself. See this test file that I made (about 7 years ago) showing the situation.

Note in particular that the dark blue div is z-index:-100, but doesn't appear below its z-index:3 parent container, nor below a different z-index:2 container that is its "uncle" (sibling of its parent).

The z-index of an element is only valid with respect to other elements using the same positioned container. Once you set position:relative on test_1 you are causing its z-index to be in a different world than the z-index of test_2. The closest you can do is set #test_2 { z-index:-1 } to cause it to appear below the content of #test_1 (but not below its background).