This is gold!!! I've been entertianing the idia but I've never had enough evidence to prove it.

But what if (as I believe) Termina is NOT an alternant demention, but a country bordering Hyrule? Then this backs up your theory even more.
(Theorizing)
The majority of the Sheikah lived in Termina, only a few lived in Hyrule. The Terminan Twili (who were called the Ikana by the Terminan Hylians) made Majoras Mask and used it to take over Termina, but acidently destroyed part of thier population with it. The servivers, thinking that the Triforce could bring back thier civilization, forged the Fused Shadows and marched to the nieboring nation of Hyrule, only a few stayed in Termina. Eventuly, Kafie would come from the small group who stayed, thus explaining his red eyes. The main group lost its war with Hyrule, were banished and the rest is history. The Sheikah that were living in Hyrule pledged themselves to Hyrule, founded Kakarico, and added the tear to thier emblem.

Hows that?

__________________