Add Shader with black texture, object is still visible

I tried to make a glow object that is only partially visible. It has an mobile/additive shader. Even when I set the entire texture to black parts of the model are still visible, I think that is where 2 parts of the object overlap, from the point of view of the camera. Can I prevent this somehow?

EDIT: I also found the old legacy add shader, when I set the tint color to black, the model disappears as expected, but then I can't make parts of it glow, because the entire texture gets overridden by the tint color.