This tutorial provides the solution you can use on any default theme like Twenty Twelve, Twenty Thirteen and any of the other default themes:
The example in this post displays the Custom Header you upload under Appearance > Header on all single posts and a custom image named non-single.jpg uploaded to your themes images folder on all other pages.
Simply change the code between lines 48 and 53 in the Twenty Twelve themes header.php file to this code:
You can easily modify the conditional tag in the code to change which header images are displays on different parts of your site.
Note: This code will only work in a child theme of Twenty Twelve. Its best practice to copy over the header.php file from your parent theme to a child theme and modify the code there which is safe when the parent theme updates.
Different Header Images On Every Page
Try the WP Display Header plugin you can search for on the plugin installation page.