diff --git a/yt_dlp/extractor/youtube.py b/yt_dlp/extractor/youtube.py
index e12f728ea3..0d3963116e 100644
--- a/yt_dlp/extractor/youtube.py
+++ b/yt_dlp/extractor/youtube.py
@@ -1496,7 +1496,7 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
         },
         # Age-gate videos. See https://github.com/yt-dlp/yt-dlp/pull/575#issuecomment-888837000
         {
-            'note': 'Embed allowed age-gate video',
+            'note': 'Embed allowed age-gate video; works with web_embedded',
             'url': 'https://youtube.com/watch?v=HtVdAasjOgU',
             'info_dict': {
                 'id': 'HtVdAasjOgU',
@@ -1526,7 +1526,6 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
                 'heatmap': 'count:100',
                 'timestamp': 1401991663,
             },
-            'skip': 'Age-restricted; requires authentication',
         },
         {
             'note': 'Age-gate video with embed allowed in public site',
@@ -4013,10 +4012,20 @@ class YoutubeIE(YoutubeBaseInfoExtractor):
                 else:
                     prs.append(pr)
 
+            # web_embedded can work around age-gate and age-verification for some embeddable videos
+            if self._is_agegated(pr) and variant != 'web_embedded':
+                append_client(f'web_embedded.{base_client}')
+            # Unauthenticated users will only get web_embedded client formats if age-gated
+            if self._is_agegated(pr) and not self.is_authenticated:
+                self.to_screen(
+                    f'{video_id}: This video is age-restricted; some formats may be missing '
+                    f'without authentication. {self._login_hint()}', only_once=True)
+
             ''' This code is pointless while web_creator is in _DEFAULT_AUTHED_CLIENTS
             # EU countries require age-verification for accounts to access age-restricted videos
             # If account is not age-verified, _is_agegated() will be truthy for non-embedded clients
-            if self.is_authenticated and self._is_agegated(pr):
+            embedding_is_disabled = variant == 'web_embedded' and self._is_unplayable(pr)
+            if self.is_authenticated and (self._is_agegated(pr) or embedding_is_disabled):
                 self.to_screen(
                     f'{video_id}: This video is age-restricted and YouTube is requiring '
                     'account age-verification; some formats may be missing', only_once=True)