Index: src/js/_enqueues/vendor/plupload/handlers.js
===================================================================
--- src/js/_enqueues/vendor/plupload/handlers.js	(revision 60899)
+++ src/js/_enqueues/vendor/plupload/handlers.js	(working copy)
@@ -461,6 +461,12 @@
 		}
 	});
 
+	$( '.upload-flash-bypass a[role="button"], .upload-html-bypass a[role="button"]' ).on( 'keydown.uploader', function( e ) {
+		if ( e.code === 'Space' ) {
+			$( this ).trigger( 'click' );
+		}
+	});
+
 	// Attempt to create image sub-sizes when an image was uploaded successfully
 	// but the server responded with an HTTP 5xx error.
 	tryAgain = function( up, error ) {
Index: src/wp-admin/includes/media.php
===================================================================
--- src/wp-admin/includes/media.php	(revision 60899)
+++ src/wp-admin/includes/media.php	(working copy)
@@ -3048,7 +3048,7 @@
 			/* translators: 1: URL to browser uploader, 2: Additional link attributes. */
 			__( 'You are using the multi-file uploader. Problems? Try the <a href="%1$s" %2$s>browser uploader</a> instead.' ),
 			$browser_uploader,
-			'target="_blank"'
+			'role="button"'
 		);
 	?>
 	</p>
@@ -3061,9 +3061,10 @@
  * @since 2.6.0
  */
 function media_upload_html_bypass() {
+	$bypass_message = __( 'You are using the browser&#8217;s built-in file uploader. The WordPress uploader includes multiple file selection and drag and drop capability. <a href="#">Switch to the multi-file uploader</a>.' );
 	?>
 	<p class="upload-html-bypass hide-if-no-js">
-		<?php _e( 'You are using the browser&#8217;s built-in file uploader. The WordPress uploader includes multiple file selection and drag and drop capability. <a href="#">Switch to the multi-file uploader</a>.' ); ?>
+		<?php echo str_replace( '<a href="#">', '<a href="#" role="button">', $bypass_message ); ?>
 	</p>
 	<?php
 }