I read the OP yesterday and wasn’t sure what this tail quiver was. Then, when I went to take a shower this morning and Charlie followed me into the bathroom - as always - and quivered his tail in the air, I thought, “Ooohhh, right! That’s the tail quiver!” I’ve always understood it as, “I’m so happy to see you!”
(No spraying around here, but both the boys are fixed.)
What ways are you thinking about?
I can think of a couple that people interpret as affection:
Bunting (rubbing their head/body against you), which isn’t affection, they are marking you as theirs with scent glands.
Bringing you “gifts”, also isn’t affection. They are trying to train you to hunt. Momma cats will bring half-dead stuff to her kittens to teach them how to kill.
Why is marking you with scent “not affection”, while quivering the tail “affection”?
Seems to me that marking one’s owner, and being affectionate, are not mutually exclusive.
More generally, when my cat sees me sitting on the couch, she jumps up with loud purrs and demands, by pushing her head at me, that I scratch her behind the ears. She then curls up against me, purring contentedly, pressing her back against me.
While no doubt each and every one of her acts has ulterior motives of some sort, the package of behaviours as a whole certainly appears to denote “affection”.
One of my two male cats, both neutered, does this all the time. My vet said it was a sign of affection. It’s not him trying to spray, because he can still do that, believe me.
Nope. Two cats, never seen it.
Does meowing insistently until I get let him get close enough that he can put his paws on my shoulders, in order to stare right at my face with an expression that sure looks like drunken love, and blissfully lick my face while purring ecstatically, count as ‘affection’?
If not it’s sure an excellent imitation! 
One of my cats (female, spayed, 6 years old) does this when she’s happy. I think it’s cute. 
How on earth do you do this? Chew on catnip yourself?
Check the pet store sites. They actually sell these. 
And when she rubs against the wall or the side of the couch, is she also expressing affection for that object?
I don’t mean to be contrary. I’m owned by a cat and volunteer with a rescue organization primarily on the cat side. I say this to show my cat-lover credentials.
Appears is the correct word. All (ok, maybe only most) animal lovers are guilty anthropomorphism when it comes to their pets. I do it even though I know better. There is nothing wrong with it as a whole (I won’t get into why it can be detrimental because that’s a different thread), but it also can be good to recognize what’s at work when cats exhibit certain behaviours because then it can help you (collective) better understand your cat.
The reason why the tail quivering was described to me as true affection, perhaps the only behaviour that is, is because it’s a body language thing. There is no claiming of territory, getting that itchy spot scratched, etc. It’s purely a physical expression of the cat’s happiness/excitement of the moment (for example: seeing you again after you’ve been gone awhile).
Well, no. Just as putting my arm around the back of a chair doesn’t have the same meaning as putting my arm around my wife.
Surely, context matters for animals as much as people. Licking a lollipop is not the same as oral sex, even though the gesture is similar …
How can one assign emotions such as happiness and excitement to a cat? How do you know they even feel these emotions at all? Perhaps they just appear to be affectionate, but if you are taking skepticism that far, why are you exempting tail-quivering?
Seems to me that if reading rubbing up against you, purring in your presence, rushing to be with you, seeking and giving cuddles as affectionate is some sort of fallacious anthromophism because the true emotional state of the animal is unknowable (and perhaps absent), the same goes double for such behaviours as tail-twitching. How can someonone on the on hand warn about “anthromorphism”, and on the other insist that some gesture a cat makes displays “true affection”? It seems to me more consistent to state that nothing a cat does displays “true affection” (or better, that this state is unknowable in an animal).
5 out of 6 cats i have/d “tail quiver”. the one that didn’t had tummy troubles.