If you have a relationship with someone, they read your body language and reciprocate. In most cases closeness and distance has to do with trust. When Aron Hakohen told a person that his friend wants to be close again the person would like his friend, as well.
A great Tzaddik once said that just like you need to have Emuna in Hashem you need to have Emuna that your friend loves you. It takes Emuna in the friendship when your friend doesn’t return a call or even got upset at you. Most broken relationships began as misunderstandings. If people would fully trust that the relationship is strong they would see things differently (just as a wack on the back can have opposite messages, depending on who wacked you).
When you do your part and try to feel the closeness deeply and truly, it will show in your body language, and will be understood subconsiously, giving that person the trust to return the friendship.