[Mithadan]

Eol's heritage may turn upon whether he was ultimately considered close kin of Thingol, in which case he is likely Sindarin, or when he entered Beleriand or turned aside from the journey West), in which case he was likely either Nandorin or one of the Avari. There seems to be no clear final conception about Eol's heritage from Tolkien's perspective.

On the one hand, he was nominally beholden to Thingol and Doriath. There is no specific mention of any other Elf living outside of the Girdle that paid a "fee" to Thingol in exchange for land. On the other hand, he was of an exceedingly dark nature, which, by impression only, seems to be like the Avari in personality. However (on the third hand...), if Tolkien's decision was to place him among those who turned away from the journey West upon reaching the Misty Mountains (as per your quote), then he is likely one of the Nandor.