diff --git a/test/test_http_proxy.py b/test/test_http_proxy.py
index a39c7651f..4ebdf0148 100644
--- a/test/test_http_proxy.py
+++ b/test/test_http_proxy.py
@@ -154,7 +154,7 @@ def __init__(self, *args, proxy_info=None, **kwargs):
     def handle(self):
         import websockets.sync.server
         protocol = websockets.ServerProtocol()
-        connection = websockets.sync.server.ServerConnection(socket=self.request, protocol=protocol, close_timeout=0)
+        connection = websockets.sync.server.ServerConnection(socket=self.request, protocol=protocol, close_timeout=2)
         connection.handshake()
         for message in connection:
             if message == 'proxy_info':
diff --git a/yt_dlp/networking/_websockets.py b/yt_dlp/networking/_websockets.py
index 46b6c7ccd..d808213da 100644
--- a/yt_dlp/networking/_websockets.py
+++ b/yt_dlp/networking/_websockets.py
@@ -265,6 +265,6 @@ def __init__(self, ssl_context: ssl.SSLContext):
         self.ssl_context = ssl_context
 
     def wrap_socket(self, sock, server_hostname=None):
-        if isinstance(sock, ssl.SSLSocket) or WebsocketsSSLTransport:
+        if WebsocketsSSLTransport:
             return WebsocketsSSLTransport(sock, self.ssl_context, server_hostname=server_hostname)
         return self.ssl_context.wrap_socket(sock, server_hostname=server_hostname)