Specifying a connection timeout for a TLS/SSL connection has no effect. Instead of applying connect_timeout for handshake ssl_do function sets timeout for session:

static int ssl_do(struct st_VioSSLFd *ptr, Vio *vio, long timeout,

                  ssl_handshake_func_t func, unsigned long *errptr)

{

 .....

  SSL_SESSION_set_timeout(SSL_get_session(ssl), timeout);

}

The SSL_SESSION_set_timeout is used for setting session timeout values which are linked to SSL resumption. They have nothing to do with timing out a connection. As a bad side effect the session hit rate goes down, especially when specifying a low connection timeout value.

Howto fix:
Check return codes of SSL_connect() function: In case of SSL_ERROR_WANT_READ/ SSL_ERROR_WANT_WRITE loop until handshake finished or connection timeout passed.