I recently felt the urge to rehook my SNES and play FFII-US (FF4) over the Christmas break. I had previously received the "Imp" and "Bomb" summons a few playthroughs ago (I even had a saved file with one of each on the cartridge), but I had a nagging feeling there were more.
I decided to check some FAQs on GameFAQs.com and discovered that there was a Mage summon! I never knew about it before, so I decided to farm it. It made sense why I never got it: it's in Magnes Cave, and when I was young, I'd just run until I got to the Dark Elf. Even in my teenage years when I replayed the game, I would just get to the Elf and leave.
I tried for several days to no avail, then decided to start keeping a text file of encounters and the number of Mages killed. (Side note: it dawned on me all these years later — 35+ — that the Mage is the "Wizard" from the original Final Fantasy.) This tracking actually helped my sanity, and eventually it dropped! (Along with the Zeus Gauntlet from the Ogres.)
I was creating this app at the same time, and in my excitement over completing FFII with all three summons, I thought I'd add it here as well.