Does he actually exist as one of the villagers, or is he a figment of Tevye's imagination who appears just to illustrate his metaphor? Tevye's the only one who comments on him and addresses him.
Back when I first watched Fiddler, I wondered the same thing. I think he is, at the very least, supposed to be Tevye's imaginary friend, or at the very most, supposed to be God.
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If I can be so pompus, I think the veiwer is God. Tevye breaks down the fourth wall and talks to the viewer when he prays, so the viewer must be God. Also, the viewer can see what Tevye can not, so the viewer becomes all knowing and omnipresent.
The Fiddler represents tradition. TRADITION! That's why the fiddler seems to appear to Tevye every time things do not go according to tradition. Then again, maybe the veiwer sees Tevye through the eyes of the Fiddler, and the Fiddler is really in control. He is actually fiddling with Tevye and the village, like God. Hmmmm!
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Can't agree with your first interpretation: (1) Tevye talks to the audience as though talking to a visitor or stranger who has just dropped into town. (2) Invariably, when Tevye talks or gestures to God, he looks up in the air off camera (in fact, a target was mounted to the camera to assist with consistency in this regard).
I always saw the fiddler as the collective spirit of the village. When they are forced to move, the village spirit goes with them. Yes, he represents their traditions, but also their will to live as a community, their love of life.