Thanks for the tip. That produced slightly more helpful output. Does this mean anything to you?
DEBUG: .../IO/Socket/SSL.pm:196: set domain to 2
DEBUG: .../IO/Socket/SSL.pm:1622: new ctx 33610976
DEBUG: .../IO/Socket/SSL.pm:339: socket not yet connected
DEBUG: .../IO/Socket/SSL.pm:341: socket connected
DEBUG: .../IO/Socket/SSL.pm:359: ssl handshake not started
(long pause again - at least 30 sec.)
DEBUG: .../IO/Socket/SSL.pm:422: Net::SSLeay::connect -> -1
DEBUG: .../IO/Socket/SSL.pm:1299: SSL connect attempt failed with unkn
+own error error:00000000:lib(0):func(0):reason(0)
DEBUG: .../IO/Socket/SSL.pm:428: fatal SSL error: SSL connect attempt
+failed with unknown error error:00000000:lib(0):func(0):reason(0)
DEBUG: .../IO/Socket/SSL.pm:1299: IO::Socket::INET6 configuration fail
+ed error:00000000:lib(0):func(0):reason(0)
DEBUG: .../IO/Socket/SSL.pm:1659: free ctx 33610976 open=33610976
DEBUG: .../IO/Socket/SSL.pm:1667: OK free ctx 33610976