To make either the wxWidgets or the wxBase tarballs build as 'base' on Linux, it's not enough just to do ../configure (it defaults to gtk), and --with-base doesn't seem to exist. The only way I've found to make it configure correctly is to add --disable-gui.
The attached patch documents this in wx2_8_Branch/docs/base/readme.txt, which presumably is the origin of readme-base-2.8.12-rc1.txt.
Also, readme-base-2.8.12-rc1.txt is missing from both tarballs...