Using these bounds, Pelinal would have had to come from somewhere between the end of the First Era and the beginning of the Third Era.
However, there may be another possibility.
Say, eventually, the Thalmor succeed in destroying Talos worship. Say that Pelinal came after the Fourth Era. Say he was a future-robot-terminator, constructed by Man to fight against the Thalmor, blessed by the Eight Divines. By some trick, perhaps a desparation move by the Thalmor to get rid of Pelinal, he was thrown back in time to the First Era, saw the Alyeids, and confused them with the Thalmor of his time.
Thoughts on this?