Index: src/wp-content/themes/twentyseventeen/style.css
===================================================================
--- src/wp-content/themes/twentyseventeen/style.css	(revision 39148)
+++ src/wp-content/themes/twentyseventeen/style.css	(working copy)
@@ -4141,3 +4141,9 @@
 		padding: 0;
 	}
 }
+
+/* For testing purposes. */
+.wp-custom-header-video-button {
+	background: red;
+	position: relative;
+}
Index: src/wp-includes/js/wp-custom-header.js
===================================================================
--- src/wp-includes/js/wp-custom-header.js	(revision 39148)
+++ src/wp-includes/js/wp-custom-header.js	(working copy)
@@ -61,7 +61,8 @@
 	}
 
 	function nativeHandler( settings ) {
-		var video = document.createElement( 'video' );
+		var video = document.createElement( 'video' ),
+			button = document.createElement( 'button' );
 
 		video.id = 'wp-custom-header-video';
 		video.autoplay = 'autoplay';
@@ -70,10 +71,18 @@
 		video.width = settings.width;
 		video.height = settings.height;
 
-		video.addEventListener( 'click', function() {
+		button.setAttribute( 'type', 'button' );
+		button.setAttribute( 'id', 'wp-custom-header-video-button' );
+		button.setAttribute( 'class', 'wp-custom-header-video-button' );
+		button.setAttribute( 'aria-hidden', true );
+		button.innerHTML = 'Pause';
+
+		button.addEventListener( 'click', function() {
 			if ( video.paused ) {
+				button.innerHTML = 'Pause';
 				video.play();
 			} else {
+				button.innerHTML = 'Play';
 				video.pause();
 			}
 		});
@@ -80,6 +89,7 @@
 
 		settings.container.innerHTML = '';
 		settings.container.appendChild( video );
+		settings.container.appendChild( button );
 		video.src = settings.videoUrl;
 	}
 
@@ -86,7 +96,9 @@
 	function youtubeHandler( settings ) {
 		// @link http://stackoverflow.com/a/27728417
 		var VIDEO_ID_REGEX = /^.*(?:(?:youtu\.be\/|v\/|vi\/|u\/\w\/|embed\/)|(?:(?:watch)?\?v(?:i)?=|\&v(?:i)?=))([^#\&\?]*).*/,
-			videoId = settings.videoUrl.match( VIDEO_ID_REGEX )[1];
+			videoId = settings.videoUrl.match( VIDEO_ID_REGEX )[1],
+			button = document.createElement( 'button' ),
+			player;
 
 		function loadVideo() {
 			var YT = window.YT || {};
@@ -97,7 +109,7 @@
 				settings.container.innerHTML = '';
 				settings.container.appendChild( video );
 
-				new YT.Player( video, {
+				player = new YT.Player( video, {
 					height: settings.height,
 					width: settings.width,
 					videoId: videoId,
@@ -119,13 +131,32 @@
 						iv_load_policy: 3,
 						loop: 1,
 						modestbranding: 1,
-						//origin: '',
 						playsinline: 1,
 						rel: 0,
 						showinfo: 0
 					}
 				});
+
+			button.setAttribute( 'type', 'button' );
+			button.setAttribute( 'id', 'wp-custom-header-video-button' );
+			button.setAttribute( 'class', 'wp-custom-header-video-button' );
+			button.setAttribute( 'aria-hidden', true );
+			button.innerHTML = 'Pause';
+
+			button.addEventListener( 'click', function() {
+				var playbackStatus = player.getPlayerState();
+				// The YT API returns 1 for playing and 2 for paused.
+				if ( 2 === playbackStatus ) {
+					button.innerHTML = 'Pause';
+					player.playVideo();
+				} else {
+					button.innerHTML = 'Play';
+					player.pauseVideo();
+				}
 			});
+
+			settings.container.appendChild( button );
+			});
 		}
 
 		if ( 'YT' in window ) {