I'm talking about the music too. In the case of the Siouxsie song, it's the melody that the guitar is playing that I find melancholic. Siouxsie & the Banshees have a lot of really melancholy songs and I do agree that this particular song is definitely not them at their most melancholy but it still has a heavy touch of it in the guitar.
As far as what I specifically think is melancholic music, as you mentioned in your OP it's music that I want to listen to on a rainy day. It usually, but not always, has a slow tempo and melancholy lyrics. But the most important thing to me is a melody and sonic texture that have a pensive quality to them. Here's another example that I love:
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