CODEX is your best friend ..
And like the codex say, if you want to add an entry to the 'Appearance'
menu , use
For Appearance: add_submenu_page( 'themes.php', ... );
or adapted to your case :
add_submenu_page( 'themes.php', 'Header', 'Header', 'edit_theme_options', 'customize_header','my_callback');
But ..:
Also see
> add_theme_page()
like so :
add_theme_page( $page_title, $menu_title, $capability, $menu_slug, $function );
Quoting from codex :
Parameters
$page_title (string) (required) The text to be displayed in the title tags of the page when the menu is selected
Default: None
$menu_title (string) (required) The text to be used for the menu
Default: None
$capability (string) (required) The capability required for this menu to be displayed to the user.
Default: None
$menu_slug (string) (required) The slug name to refer to this menu by (should be unique for this menu).
Default: None
$function (callback) (optional) The function to be called to output the content for this page.
TL;DR version
All the above said in general for custom menu entries, but in the specific case of custom header, all you actually need to use is :
add_theme_support( 'custom-header' );
See details here : http://codex.wordpress.org/Custom_Headers