I found Alfgar tonight in Uldah! It was 9:15PM CST on Besaid.

He was standing right in front of the fountain between the repair NPC and the chocobo handler.

Woot!

Edit: As of 9:35PM, he's still here. Not sure how long he remains. If you're on Besaid and still need to talk to him, better get to Uldah!