Index: src/wp-includes/theme.php
===================================================================
--- src/wp-includes/theme.php	(revision 39202)
+++ src/wp-includes/theme.php	(working copy)
@@ -1400,7 +1400,7 @@
  * @return bool True if a custom header is set. False if not.
  */
 function has_custom_header() {
-	if ( has_header_image() || ( is_front_page() && has_header_video() ) ) {
+	if ( has_header_image() || ( has_header_video() && is_header_video_active() ) ) {
 		return true;
 	}
 
@@ -1408,6 +1408,22 @@
 }
 
 /**
+ * Checks whether the custom header video is eligible to show on the current page.
+ *
+ * @since 1.0.0
+ *
+ * @return bool True if the custom header video should be shown. False if not.
+ */
+function is_header_video_active() {
+	$video_active_cb = get_theme_support( 'custom-header', 'video-active-callback' );
+	if ( empty( $video_active_cb ) || ! is_callable( $video_active_cb ) ) {
+		return true;
+	}
+
+	return call_user_func( $video_active_cb );
+}
+
+/**
  * Retrieve the markup for a custom header.
  *
  * @since 4.7.0
@@ -1436,7 +1452,7 @@
 	}
 	echo $custom_header;
 
-	if ( has_header_video() && is_front_page() ) {
+	if ( has_header_video() && is_header_video_active() ) {
 		wp_enqueue_script( 'wp-custom-header' );
 		wp_localize_script( 'wp-custom-header', '_wpCustomHeaderSettings', get_header_video_settings() );
 	}
@@ -2048,6 +2064,7 @@
 				'admin-head-callback' => '',
 				'admin-preview-callback' => '',
 				'video' => false,
+				'video-active-callback' => 'is_front_page',
 			);
 
 			$jit = isset( $args[0]['__jit'] );