My Eos issue..

[Anatha]

I've never once had her fail to respond to a manual command to use embrace on a target. It'll simply either cast immediately or when her GCD refreshes.

[Ceodore]

Personally, to avoid having Eos just go crazy in fights, I pair her Embrace onto a macro with Physick, no interrupts, nothing fancy, just

/ac "Physick <t>
/pac "Embrace" <t>

In the likely scenario where the tank is taking consistent damage, I'm probably going to be spamming quite a bit of healing anyways, so just pressing this macro over and over usually makes her focus on what I am focused on. I also have a much more advanced macro for the other skills, but this is just kind of my spam heal. This macro also takes care of the fact that her CD on Embrace is 3 seconds and mine on Physick is only like 2.38 seconds. It will just ignore my cast when I am on GCD and still make her cast, or it will ignore her cast on her GCD and still do my cast, and when we both are up to cast at the same time, it will do both.