video header in desktop view, image header in mobile view

First, add video header support on your theme.

add_theme_support( 'custom-header', array(
    'video' => true
) );

Next, add the_custom_header_markup(); on Header area where you want to show the image / video header.

Finally, style your video header with some css like this.

.wp-custom-header iframe,
.wp-custom-header img,
.wp-custom-header video {
    display: block;
    height: auto;
    width: 100%;
        height: 400px;
}

The header will auto-switch to Image whenever user accessing your site from mobile devices. No need to add extra code to handle video / image banner switching.

Source

you can use the wp_is_mobile() to check if the user is viewing from mobile..

So, the code becomes:

if(wp_is_mobile()){
  //show image
}
else{
 // show video
}