Sorry about the confusion. My point is really as expressed in the second post; it's just coincidental that one eye is activated at the same time as the other.
I now understand what's going on - clones
and Beethro (as demonstrated in the example hold, and this is replicable in other situations too) lose invisibility when not active, allowing them to behave like decoys.
It seems to me that they shouldn't. After all, Beethro has drunk the potion, and once you switch back to him, he's still invisible. Furthermore, invisibility is inherited by clones, which is evident when you stitch to them. Why anyone should lose it is unclear. Admittedly, one could make some cool puzzles from this (limited, I think, solely to the interaction with eyes), but still...
So my answer to your question number 2 is Yes, in my view. (I'm assuming you're referring to what happens when they're inactive)
About question 1 - I'm confused, can the clone be different to the player (e.g. goblin player with Stalwart/Beethro clone). I've never been able to generate this, and if not, I don't understand what you mean. If the behaviour is that cloned goblins activate evil eyes, while goblins (player goblins, that is) don't, then this is counterintuitive.
I get the feeling I'm not understanding question 1. But I'd say that clones of the player should activate the eyes in the same way the player role would.
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