When someone says that someone doesn't
blink. It means they don't think twice or they won't hesitate about committing a certain action. It most commonly refers to murder but it could be used for other things as well like stealing or firing someone. Things most people may feel guilt or uncomfortable with but doesn't phase these people in that particular circumstance.
The term mostly likely came from how people
squint at the sight of bright
gunfire after while you get use to it and the there's no need to squint or blink.