Haha, poor bird and its terrible AI. I agree it could use some "brain restructuring". I personally use mine as purely DPS mode to prevent it from doing too many weird things, but even then it spams Stun so often that if there's a mob you actually need to stun, your dear companion has made sure the mob is resistant to it at that point. Always awkward when Chimeras are involved, but thankfully it's not something that comes up often.

How about making Gysahl Greens a key item instead? The functionality would remain but it'd free up the space in your inventory and it sounds like it'd be fairly easy to implement. They're very cheap and can be bought anywhere, so I'm not bothered about buying 100 of them and forgetting about it.
A skill is good too, but having more random stuff in my hotbars or having to navigate the menu every time I want something (like the Dig skill) is annoying to me personally. Maybe it'll be easier to manage with the special hotbar they're adding soon, but a key item would be the most elegant solution to me.