The other possibility is that the Eternal Sharingan just works THROUGH the mask, and we wears a one-eyed mask so he can use his Sharingan without revealing that he even has it(if it's possible to turn on one and not the other).

Like if the whole time he's fighting these Konoha ninja, he just seems like normal Tobi, but the whole time, the eye Sharingan behind the mask has been on and working.