Index: src/wp-includes/class-wp-customize-manager.php
===================================================================
--- src/wp-includes/class-wp-customize-manager.php	(revision 39531)
+++ src/wp-includes/class-wp-customize-manager.php	(working copy)
@@ -3889,7 +3889,7 @@
 		$this->add_setting( 'external_header_video', array(
 			'theme_supports'    => array( 'custom-header', 'video' ),
 			'transport'         => 'postMessage',
-			'sanitize_callback' => 'esc_url_raw',
+			'sanitize_callback' => array( $this, '_sanitize_external_header_video' ),
 			'validate_callback' => array( $this, '_validate_external_header_video' ),
 		) );
 
@@ -4312,6 +4312,18 @@
 	}
 
 	/**
+	 * Callback for sanitizing the external_header_video value.
+	 *
+	 * @since 4.7.1
+	 *
+	 * @param string $value
+	 * @return string
+	 */
+	public function _sanitize_external_header_video( $value ) {
+		return esc_url_raw( trim( $value ) );
+	}
+
+	/**
 	 * Callback for rendering the custom logo, used in the custom_logo partial.
 	 *
 	 * This method exists because the partial object and context data are passed