Also to add onto the 2nd post.
When your Guild reaches level 4 Eidolons will spawn everyday except for Sunday throughout the day.
There are 5 platforms, each one has a chance to spawn different Eidolons, and the Cube that summons the Eidolon will randomly spawn above one of the platforms giving you a hint on what Eidolon will spawn.
They spawn as level 50, but are fairly stronger then the Eidolon Temple version and can take 2-5 players to kill depending on which one spawns.
Here is a picture of the times, the time is in GMT -5.
The Treasure charms in Loyalty Shop can also be used when you kill an Eidolon to give you bonus loot, so I would suggest using those if you want the Eidolon faster.