All Eidolons have an arcane skill, which is a special skill with an orange/gold border around it. The effects of those skills vary between Eidolons. The arcane skill system itself can be equated to playing a matching game: select the same energy type as the Eidolon's current energy sphere.
Types of Energy Spheres
There are 4 types of energy spheres: Free, Infernal, Glacial, and Vital. The free energy sphere acts as a wildcard, in that any of the 3 types of energy will correspond to it.
Accessing Arcane Skills
Each Eidolon has 1 to 4 energy spheres, which are the spheres that are next to the HP bar when in combat. In order to gain access to an Eidolon's arcane skill, that Eidolon must be down to their final energy sphere, which is the same type as the Eidolon itself -- all Infernal Eidolons will have their last energy sphere be Infernal, all Glacial Eidolons will have their last energy sphere be Glacial, and all Vital Eidolons will have their last energy sphere be Vital.
(Note: When using Auto Combat, the system will use the most effective options for arcane use in combat )
Consuming Energy Spheres
Energy spheres are consumed from top to bottom. The concept itself is very basic; to consume an energy sphere, you just need to select that corresponding energy at the start of the round. Once all energy spheres have been consumed, all of the Eidolon's energy spheres will be reset.
Triggering Arcane Skills
Once an Eidolon is down to its final energy sphere, all you need to do is select its corresponding energy at the start of the turn and the Eidolon will use its Arcane skill. Using Nemesis as an example, once she is down to her final energy sphere (Vital), I can trigger her arcane skill at any time by selecting a Vital energy at the start of the round.
Free Energy or Less Spheres
As a general rule of thumb, the more Free Energy spheres an Eidolon has, the easier it is to use its arcane skill. However, do note that having fewer energy spheres doesn't necessarily mean that it will be faster to trigger an arcane skill (barring Eidolons with only 1 energy sphere). While you could technically fire off an arcane skill every other round, it may be detrimental in the long run.
Lets look at Perseus' arcane skill: Enchanted Guard.
While Perseus only has 2 energy spheres, you'd have to use a Vital energy first before you can use an Infernal energy to trigger that arcane skill. While that may be fine if you only have 1 Eidolon on your formation, the same can't be said when you've got 5 Eidolons with different elements and are trying to activate your mount skills while also trying to prevent your opponent from activating their mount skills.
Tl;dr: in terms of frequency, unless you've got some insane synergy between the Eidolons in your formation, arcane skills that don't have free energy become situational instead of spammable.
Every turn should bring at least 1~2 (ba