I own an original VHS Tape of that movie and I really like it a lot.
The music is great indeed, the whole soundtrack was performed by german band Rheingold.
The story so far is about a young girl getting crazy for a musician (played by Bodo Staiger from Rheingold) There were a lot of discussions back in the 80s about that movie, because Desiree Nosbusch was naked in some scenes…
That she killed her “idol” with a candleholder or a knive (I don’t remember exactly…) was no problem…
It’s not that much german new wave, I would recommend these films more then “Der Fan”:
Decoder (1983) (with Genesis P.Orridge, F.M.Einheit)
Kalt wie Eis (1982) (with Blixa Bargeld, Thomas Voburka etc…)