It doesn't appear at the rhs.
The search box is a block, in the header position.
With stock, header for our theme (garland) appeared above everything. Now it works for at least firefox...
This is configured by the CSS associated with the theme, garland, which is found at: public_html/testdrupal/themes/garland/style.css.
page.tpl.php was also edited to move the header-region div inside the container.