So... what about the Behemoth FATE ?

[Astrahime]

There is many fates that works like this

Ixion, the robot mount in Shadowbringers and levelchecker in Endwalker to name a few

Ixion has the weather, and is only in one zone, and has only a few possible spawn locations.

Foxy lady is the one that's lacking the weather and is thus this level of difficulty.

Though the weather that makes some of them easy, does seem to have stopped. I can't remember there being special weather for either of the shadowbringers ones, and endwalker seems to be another set of nopes. So it looks like it's going to be just "get lucky" from here on out.

Behemoth, Odin, Couerlregina, Proto Ultima, and Ixion.
Behemoth is the only one that doesn't have a weather telegraph, but you can also get behemoth horns from Eureka Pagos. It's also the only way to get Behemoth Pelt.

The SB/ShB/EW rare FATEs are a lot easier than you'd think to spawn.
Because you need to spawn them manually.
Foxy Lady? 2 NPC FATEs which then spawn another FATE that will then spawn Foxy Lady in 5-30 minutes.

A Finale Most Formidable? 2 different chain FATEs.
The Tail, The Head, The Whole Damn Thing? A 5-FATE chain that usually resets at the 4th one.
Devout Pilgrims vs Daivadipa? A 2-FATE chain.
Omicron Recall: Killing Order? Again, a 2-FATE chain.
Plus the ShB/EW ones spawn in a single location and their boss is visible far away in the overworld.

If you're having issues finding these, consider joining a discord or CWLS that's interested in this kind of thing.
Centurio Hunts and Faloop both have discord bots in their servers that ping whenever someone calls out a rare FATE (and faloop users may also ping for previous expansions' FATEs that just give an achievement, like the one in Yanxia that gives you a DRK glam weapon) - Faloop even has its own website that tracks when rare FATEs spawned last and how long it'll be till it might spawn/can be spawned again.
It's only "luck" if you don't know what you're doing.