I also couldn't figure this out, I saw a post from LAGS saying that you need both parts "You will need all two parts of the doll. One is in sunflower city and the other one is in the asylum map." and I have the penis part and the ass part but nothing happens.
I remember in a previous version it worked fine, you'd go into the gallery room and occasionally see the doll doing stuff. But in the recent builds I've not seen anything at all.