So, what does it mean?
When I think of it, I imagine someone holding it between their index and middle fingers.
To not take deep lung filling drags.
Just about every smoker I’ve ever met (including myself) does it like that unless they are smoking a left handed cig. 
Could FS have meant “Holding it between their index and ring finger”
This I have never seen.
The image that comes to my mind is taking a puff, then holding the cigarette hand off to the side, with the palm forward and the cig pointing back. Knead to Know’s three masculine examples held the cigarette forward of the face.
I’ve only seen it a handful of times. I think it’s always been Asian people doing it…but that’s probably just a confirmation bias.
There’s a “super-macho” way to hold a cigarette; wish I could find a photo. The hand is in what I’d call a semi-fist, with the thumb and index finger making somewhat of a circle, and the other fingertips lined up with the index finger. The cigarette is held between the side of the thumb, right next to the nail, and the tips of the index and middle fingers, sometimes including the ring finger.
Another “macho” pose is just to keep the cigarette in the side of the mouth.
And “like a girl” could also mean taking dainty puffs, rather than long drags.
I think more of holding towards the end of the fingers rather than the more masculine past the first knuckle. Also straight or even curved back fingers instead of curled.
Combine all three of those and it’s definitely feminine.
That seems like a possibility. I also think of either:
(a) Holding the hand palm upward so that you are practically cupping your chin in your hand while taking a puff. (Then pulling the hand away but keeping it in that position while you exhale.)
(b) Wrist bent forward, fingers straight and bent as far backward as possible; thumb and pinky pointing out to the sides like wings.
Bogey used to smoke like that. I see it a lot in older movies.
We always called this the “European” way of smoking. Where “European” was a nice way of saying “swish.”
I think it’s the (aggressively sexy) way of holding the elbow of your smoking arm in your non-smoking hand, and then puffing away. Preferably while wearing a hair net and looking up. See “his girl friday” or Terry Pratchett’s “The Truth”.
I had a friend who always laughed that I “smoked like a girl.” When I asked her what she meant, she made it clear that she thought it hilarious that I was holding the butt between my index and middle fingers, as opposed to “Bogie style.”
Todd Glass used to do a great bit about how his dad would smoke “like his face was hurting him.” Wish I could find it on YouTube…
Here’s one example – http://whattamisaid.blogspot.com/2009/09/sexism-makes-me-hate-betty-draper.html
Think limp wrist…it can flop either backwards, as in the above picture or forwards.
I always thought women tend to hold thier cigarettes higher and farther away from thier bodies as if they were trying to avoid the smoke coming off the cig. My theory being, they are more concious of whether they reek of smoke than men and try to avoid coming in contact with the smoke beyond what the act of smoking actually requires.