My own research bridges somewhat on these topics, and I would suggest adding the following people to your considerations:
Hegel - specifically the idea of mutual recognition. Within this, I think it's pretty obvious that Sartre is thinking of "Herrschaft und Knechtschaft" when he's writing about the look in Being and Nothingness. Specifically, the echoing of unhappy consciousness as bad faith supports the claim of symmetry.
For the Other, I don't think Levinas can claim originality for this, but he is, as far as I know, the first person to write about it specifically in phenomenology. Martin Buber's I and Thou and Soren Kierkegaard's pseudonymous Sickness unto Death both have similar ideas of an other that is above me. Buber and Levinas communicated and argued in writing specifically about the relation to the other and whether its transcendent.
Merold Westphal has a book Levinas and Kierkegaard in dialogue that treats on a lot of the ways their thought relates. The claim I think most accurately captures how Levinas relates is that at times he seems like a very skilled reader and at other times an unbelievably bad reader. The influence of Kierkegaard if any seems to have been indirect prior to Levinas developing the core of his idea.
There's two reasons I can imagine for this behavior on Levinas's part. First, there's a soft rule in philosophy that the accuracy of a philosopher's reading of another philosopher is inversely proportional to their fame. i.e., the more famous the interpreter the less accurate to the original thinker. Second, Levinas needs to keep his position distinct in order to have any novelty that makes him worth listening to.
A third and likely source of influence on Levinas is Heidegger and the notion of Being and the way in which Heidegger uses the concept of Gegenstand with reference to the beings that stand before us vs. the Being that is kind of withdrawn. Unfortunately, I haven't written much about this area in quite some time so my knowledge of the best sources is poor.