In case future searchers find this page, as I did, not by looking for ways to change the header as described above but for ways to add my own image to the list offered under Theme Options as “Background”.
This list is in \wp-content\themes\gear\functions.php. In functions.php, look for an array that starts at about line 51, listing the options offered by the “Background” pulldown such as “Two gears (yellow)” and “Shiny”. Each of these items also specifies the address of the image it uses. Add your own line to the array, naming your own background and specifying where the image is that it should use.
Put the image where you say it should be.
Upload the image and functions.php.
Login to your Admin account for the blog; under “Appearance” open “Theme Options”; in the “Background:” pulldown select the item you just added; click “Save Changes”.
Visit your blog as a user and see your new background image.
