What's the exact meaning of 'unblinking gimlet intensity'?

In The Guardian review of the 2024 movie The Apprentice, Wendy Ide describes the performance of actor Jeremy Strong like this:

...widely feared rightwing lawyer Roy Cohn (Succession star Jeremy Strong, bringing his trademark unblinking gimlet intensity to the performance, with chilling effect)

(emphasis mine)

Oxford Advanced Learner's Dictionary states that gimlet can be used figuratively as:

eyes like gimlets (= looking very hard at things and noticing every detail)

I assume Ide uses gimlet in quite a similar manner. But does she mean that Strong in the movie doesn't blink his eyes at once and looks very hard at things, or the fact that the audience won't blink at all when watching Strong in the movie?

It is a reference to "gimlet eye", a penetrating look. Named after a tool like an awl. Nothing to do with the audience; the text says "bringing his trademark unblinking gimlet intensity to the performance" [my emphasis].

The definition related to the gimlet eye that you cited is a poor one; a gimlet eye refers to a steady, penetrating, open-eyed (i.e. unblinking and unsquinting) stare. Perhaps with a better definition you would not have thought that it somehow described the audience. It is the actor who brings "intensity" to a performance.