I've written about the auto-erotic in the feminine position (object egoism and subject altruism). In my experience Fairbairn is right. There is an 'as if' quality to the object egoist who utilizes the impressions she has of others and there is whole sale adoption of something in the personality of the beloved with the subject altruist.
In both expressions the face has shown up in dreams or from associations. In my experience the face will also be paired with some kind of darkness. These self-other units are always important and to ask the person to describe the darkness and get adjectives like empty, cold, etc. to be used as I statements is important.
Fairbairn wasn't dynamic enough and what he was describing as "schizoid" phenomena is sometimes projective identification in which the person assumes the place of the parental imago. The parental imago of Death at this early stage is just emptiness and coldness.
I don't think the face is the deutero object of the auto-erotic stage, like hand, anus, or phallus is. I still have to point out that it seems wrong to use these stages since they are also the masculine and the feminine has its own zones.
Additionally, the face sometimes reveals its importance in relation to a mask.
Interestingly, masks, shoes, and hats and other things seem to often represent the phallus for the feminine. The importance of having many shoes often indicates the importance of the feet as a displacement of the penis in some women, for example.
It's a good rule to ask for thoughts about the body part that is covered up by an idiosyncratic item that appears in a dream or that is emphasized in stories.