Okay, here is my personal guess about the Twili.
I think the tribe that has the most potential to be conected to the Twili are the Zuna...
Yeah the Zuna, never heard of them? Okay I don't blame anyone, they only appeared in
FSA and there village was so small you could pass it in 5 seconds.
These are the zuna people:
And these are the Twili:
Guess what, I didn't find a single picture of the uncursed Twili..:/
Well never mind, I only wanted to outline some physical similarities:
-They have similar bodyshapes
-greenish skin
-they feature similar high pitched but soft voices
-They a have a similar clothing style
-They share dark markings under their eyes
But there is more then these physical similarities:
FSA talks about a dark tribe that tried to invade Hyrule and was sealed in a Mirror.
The Zuna tell us that their ancestors built the Pyramids in the desert. Said pyramids hold and evil artifact, namely the trident of power, created by an evil/dark tribe.
It's not proven but I find it very likley that the Zuna and the Twili share their ancestors.
Anyway back to the Sheika -> Twili thing:
This is the back of Midnas helmet
There it is again the eye-symbol, but as others have allready said the eyesymbol is not a Sheikah only symbol.
I personally doubt that the "dark interlopers" were a single race.
The Twili feature the typical gerudo hair (bright orange) and snakes seem to be their royal symbol (almost everything Twili related has snakes on it), the only other race that has connections with snakes are the Gerudo (spirit Temple and arbiters ground statues).
The Gerudo are also the only race that has been actually seen preforming black magic.
My personal guess is that the interlopers were either the Zuna's ancestors or a multiracial group of renegades.
Both the Sheikah and the Gerudo share similarities with the Twili. Both of them seem to be able to preform black magic.
But wait Lanayru shows us three dark figures as a representation of the Twili ancestors. Does each Dark Link represent a different race? If that should be the case, who is the third race?
They have to be able to interbreed with Sheikah and Gerudo and are probably also skilled in magic. There is only one race left, that meets those conditions, the Hylians.
So the Twili ancestors could be a Gerudo, Sheikah (and Hylian?) mix.