Since this is about me, I will answer.
Is there a ping etiquette?
Not that I know of.
Ping etiquette should follow what would be socially acceptable in real life situations. If you would jump into a conversation in real life, you should feel free to do so in comments. I believe comments are fair game.
Bonus question: if A and C are having an argument below a post (not in Chat), is there a rule against B saying anything?
No. I haven't seen any rules about pinging itself. But on the site, there's an overarching rule to be nice. And again, what you would do in person in the real world should apply.
As a moderator on another site, I often have to jump in and remind someone to be nice. Or jump in and ask for proof. Or jump in for other reasons. But that is in my capacity as a mod. As a user and reader of comment threads, I do jump in to disagree when it seems appropriate, sometimes even when it doesn't, but I usually regret those and delete the comment (with an apology, but that's me. And I'm no saint.)
In the real world, we don't get upvotes for our comments. I've seen comments that were incredibly unkind get lots of upvotes. The point is, what would certainly not fly in the real world flies here pretty often. But it's not nice.
In summary, comment threads are fair game for anyone reading them. We live in community here as in real life. But our behavior online is often far from what we would do in real life, so let that guide you to some extent. And remember to be nice.
If there is nothing in your pings which isn't polite, then the social behavior applies.
Now about this exchange specifically.
Please allow me to point out that the conversation did not go quite as written. To the best of my ability to recall (which isn't so wonderful any more, but if it is very important, I can ask a mod to release those comments to me):
- I was commenting to the author under a post written by them, disagreeing with one point. It was very polite. I was not in any way badmouthing anyone. (And there were maybe 6-7 pings, not the "one-and-shove-off" recounted.) The conversation was more or less finished when the first ping from B appeared.
- B questioned me about the veracity of what I was saying.
- I answered B that I had seen it myself.
- B replied that they did not believe me, and that the person whose post I was commenting on was unaware of doing what I said. (B was speaking for someone else in their presence.)
- I said, "They are aware", and to read x post which supported what I said.
- B asked for evidence. B stating something to that effect that the whole community deserved evidence.
- I stated I could not give B evidence, because the source was not available.
- B repeated themselves, stating their opinion that the writer of the post was not aware of such and such, and that B and everyone else wanted evidence.
- I answered B again, stated that I saw the comment the first time, referred B again to x and having answered, I said, "Please" don't ping me again.
- B pinged me again saying I could not possibly be correct.
- I answered B again in different words, and repeated, "Please" don't ping me again".
- B pinged me again stating their opinion.
- I answered, "You (B) believe one thing, I the opposite, but only one of us is right", and asked B not to ping me again (please).
- B asked the poster to reply to my assertions.
- The poster ignored the comment.
- B then pinged me again with an observation and question.
- I didn't answer; I just asked B not to ping me again.
- B continued the comment thread without me.
N.B.: Every time I asked B, I asked B politely, "Please don't ping me again."
Someone in a thread only has a few options when they are pinged. They can answer, they can ignore, they can announce that they are disengaging, they can ask that you not ping them again.
Most people just start to ignore someone in a thread who is insistent on getting an answer. There is a reason I specifically asked B not to ping me. I know that B has difficulty letting go. So I was signaling B that it was best to let go. I don't like to just ignore people when I believe them to be sincere. When they are being rude or insincere, I have no problem ignoring them by simply disengaging with them.
So is there a ping etiquette? I don't think so; I've never seen one. I haven't seen it from anyone else, and I myself have rarely asked anyone to stop pinging me. But I believe B was sincere, and that I should not simply pretend B didn't exist.
You're asking, in effect, if B was wrong in any way. I'd say B was... not being nice. I repeatedly asked B politely to stop pinging me, but they did not. There's no absolute right or wrong, and no rules. More like a "Treat others as you would be treated situation". Since B and I have different expectations, there's no black and white answer.
If you want opinions on the rightness or wrongness of the situation you presented, in meta the usual is to look at how the votes go.
I can produce evidence for my side, so please represent things accurately when you ask for support in meta. An honest answer will help people more than one answering a question framed specifically to be sympathetic to your bias.