As shown here. (O.O2)
Does that device (which looks like a simple pocket watch) play any part of the "Doomsday device"? I've wondered about that for years.
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Seems like it's supposed to be a spy camera. It was a common trope in the 60s that a camera could be hidden in a watch or similar small object. Note the shutter click noise when he pushes the lever, and then turns the knob to advance the film.
I found some discussion on The Straight Dope Message Board as to why he would do that. A common opinion is that he's such a committed Cold Warrior that he wants to spy on the American War Room even when it's absurd because everybody is about to die.