Every rule is made to be broken. Usually, we would say "since you went away" (past simple). However, that would make the listener think about the moment the person left. The songwriter is much more interested in the feelings she experienced AFTER the person left. You could express that in normal speech by saying "now that you are gone" (present tense of "be" with "gone" as an adjective). However, that might sound like the person is not going to return, and that is not the meaning the songwriter wants. Since the songwriter is more interested in feelings than grammar, she uses tenses in a way that we usually wouldn't to better convey her precise feelings at a specific moment: she wants to show that her feelings changed AFTER the other person left, but she hopes he will return soon. The strange use of tenses emphasizes the strangeness of the emotions she is feeling at this particular moment.