Yes it only damps the open strings. It does damp them pretty evenly though. If you want less sustain on the fingered notes you can just release the note. And as I mentioned I can push it out-of-the-way when I don't want it engaged. I'm not saying it's the only way to do it. Maybe the rubber thing works for you. It depends on what you're trying to achieve.So basically a piece of foam that gets pressed against the strings at the nut by a Velcro tape around foam and neck?
That would damp open strings only (and the out strings more than the inner ones). I used a piece of thin rubber between fingerboard and string close to the nut for that purpose (and in my case only for my high C string and only if I use a steel core one which is seldom the case).