A lot of these sayings are exaggerations.
"If she blinks, kill her" = If she makes a move, kill her/if she tries to escape, kill her. It's more for the prisoner than to the guard, as though saying to the prisoner, if you dare try to pull anything on us, we'll hurt you so stay put.
"Keep a close eye" = watch carefully.
I find it's helpful to view a lot of these sayings as exaggerations with their meanings trumped up so they are driven into someone's mind...strangely enough, that method turns these sayings more sensible 
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Said the apple to the orange,
"Oh, I wanted you to come
Close to me and
Kiss me to the core."
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