Okay, I realize this is extremely late, but I've always been fascinated by this NM. Long time reader, first time poster.
Anyway. I've been doing testing on my own FFXI server (that I made with ProjectXI)
On the server, NMs are always up. Regardless of time or spawn condition or placeholders. Argus and Leech King are both up at the same time for example:
http://i33.tinypic.com/2nsaozq.jpg
http://i36.tinypic.com/2hntdlc.jpg
Jormy, Nidhogg, Fafnir, all spawned NMs, everything is always up.
However, one NM in particular, that has only ever been seen on the Atomos test server, does not appear. Voluptuous Vilma.
This leads me to believe that it was tested on that server, and deemed unnecessary/useless and later removed. The overgrown rose is always in the same spot, and rose garden is off to the side, ready to jump into Overgrown rose's skin/spot when the time condition is met. Vilma is nowhere to be found.
http://i38.tinypic.com/2ypajbk.jpg
How does this relate to Almight Apkallu?
After jumping to the boat zones, all boat NMs are instantly up, except two. However, fished mobs are sometimes hidden beneath the boat zone. Since everything on my server is true aggro unless you're on a chocobo, just zoning into the boat will cause almost everything to aggro you on the manaclipper-style boats. Going belowdecks will cause the same thing to occur on the ferry-style boats.
http://i35.tinypic.com/2mmhkjk.jpg
http://i38.tinypic.com/346szf6.jpg
Almighty Apkallu and Proteus are the exceptions to this.
They never load on the nashmau/alzahbi boats. Ever. This leads me to believe that they are both triggered to spawn by something that a fake server would not able able to have information on. This means it can't be time, weather, day, placeholder, length, force pop, etc.
This also means Proteus and AA are somehow linked.
Yes, Proteus has spawned many times. But no matter now many times I reloaded the zone, checked everywhere in the zone (including underwater, in the air), killed everything, etc... It just wouldn't pop.
Same thing for AA. He just never pops in any regular way.
This would also explain the similarities to Proteus and AA in NPC list. Both of them, go:
Air Elemental
Thunder Elemental
Proteus/AA
There must be some differences making Proteus spawn more often. Or perhaps they're both glitched, the bird being more glitched. Who knows? However... I was thinking the frequency of ships taken from Whitegate -> Nashmau (much, much higher) may have something to do with more frequent Proteus spawns. Since my server doesn't keep track of how many times I ride the boat, it may be possible. The numbers for Nashmau -> Whitegate, as SE stated, are far far less. Could be something like: Ship ride #1000 = spawn
Food for thought.
Perhaps this solves the mystery. Perhaps not. I just hope this helps somewhat, as I am an Apkallu and Blue Gartr fan.