At the end of chapter seven, Luzzatto presents what is probably the best know Jewish technique for effecting change. Luzzatto did not discover it - the Chinuch described it over four centuries earlier - but it is so basic to Judaism it is hard for anyone to really claim it as their own.
Whether you use the Chinuch's formulation, האדם נפעל כפי פעולותיו, or Luzzatto's, החיצוניות מעורר הפנימיות, the idea is the same: what we do molds who we are. Luzzatto harnesses this reality in the effort to acquire Zerizus.
Just as Zerizus is the result of an inner excitement, so too will Zerizus produce an inner excitement. That is, one who rouses himself in the performance of a Mitzvah, as he quickens his outer movements he also causes his inner emotion to ignite, and his longing and interest will strengthen and grow. But if he moves his limbs lethargically, then so will his spirit die down and be extinguished. Experience attests to this.
Now, you already know that what is most wanted in the service of the Creator is the interest of the heart and the longing of the Neshama... However, someone in whom this longing does not burn as it should is well-advised to get himself into in by force of will (i.e., fake it), which will naturally result in the development of this longing. For the external movement inspires the internal and the external is surely more under our control than the internal. Making use of that which is in his hands, he will, in turn, acquire that which isn't. For inner joy, interest and longing will be born of the passion he invested in his free-willed movements. (translation based in part on Machon Ofek)
Luzzatto is telling us that inspiration is a science. If we learn its laws we can manipulate our inner reality.
The only remaining question is why. Why is the internal affected by the external? In the physical sciences, such questions are beyond the pale. A law of nature is just that; we cannot ask why
E=mc2. I submit that my question may not be legitimate. Nonetheless, I have a hypothesis.
In true Jewish tradition, I begin my answer with another question. This entire discussion presumes that the self actually consists of two different identities, the "external" and the "internal." Luzzatto preceded Freud by more than a century. Which two selves is he referring to?
I believe Lazzatto is referring to the well established duality of the body and the soul. It is the soul that will respond to and mimic the behavior of the body. As Luzzatto wrote in the quote above, "What is most wanted in the service of the Creator is the interest of the heart and the longing of the Neshama..."
Luzzatto spoke of this longing of the Neshama back in chapter one. There he cited a Midrash which compared the Neshama to a princess who marries a commoner. Just as this simple man will never be able to satisfy the princess, so too is the Neshama trapped in an unhappy marriage. Ever yearning for her spiritual home in Heaven, the Neshama suffers constant disappointment and dissatisfaction with her host body and the material nature of this world.
Now, the location of the soul in our bodies is not limited to our minds or our hearts. "Just as the Holy One, may He be blessed, fills the entire universe, so too the Neshama fills the entire body" (Berachos 10a; cf. Nefesh HaChaim 3:2). It follows that whenever we make a move, the corresponding "limb" of the soul is forced to make the very same move. The "I" of the body is literally the puppeteer of the "I" of the soul trapped within!
This explains why the external inspires the internal. Doing Mitzvos lethargically doesn't elicit a soul response, for such Mitzvos leave the soul cold. But when we perform a Mitzvah passionately, the Neshama awakens. As the body puts her through the motions, the Neshama finds happiness in a holy act done right. And, for that one moment at least, the princess finally makes peace with her husband the puppeteer.