The Third Connection is accessed via the small window in the middle left part of the Seventh House screen. This can only be done once The Third Gateway has been opened.
To solve the puzzle, form a sentence by selecting letters. Each letter is attached to one or more nearby letters, so subsequent letters can only be selected if they are attached to the currently selected letter.
In this puzzle, 8 letters can be selected more than once, and 1 letter is not what it appears to be.