The Noam Elimelech towards the end of his commentary on Sefer Shemoth explains that the word Mishkan is from the word HamShachah, meaning to draw out or draw down. The Mishkan is peculiar in that it was always meant as a temporary edifice. In this sense the Mishkan represents the Reshimu, the imprint of the eventual drawing out of HaShem's godliness into the world.
The function of the reshimu is to give direction and shape, to flesh out the light that will flow into it. Just as liquid takes the shape of its container, the supernal light comes down taking the shape of the reshimu into which it is drawn. The creation of the world itself was a process of HaShem shining His divine light into the reshimu He had created through first clearing a (figurative) space in which to create the world.
From this perhaps we can see why Sukkah is learned out from the Mishkan. They share the same goal. In our yearly life, the Sukkah is the imprint of how we are going to relate to HaShem through our surroundings. From Shemini Atzeret and onwards through the rest of the year we are working on drawing down HaShem's light into the reshimu that was created over the seven days of Sukkoth.