To open the Second Gateway, open The Seventh Hex, where there should be a small pink blinking square in the image at the top of the screen. Click this square.
You will be returned to the Seventh House, where a pink path will appear moving in a circuit around the screen. Put your cursor over the path and trace it from start to end. If you move off the path, you will need to start over, so take your time and go slowly (there does not appear to be a time limit involved with this).
Upon successfully tracing the path, a new puzzle called The High Priestess will open.