It's concrete, because the book says an official's count may be used.

Maybe your assignor is happy. I have a couple who would not be happy.

I say put 18.0 back on the clock. You can say you know it took 5 seconds to break up the skirmish. If anybody asks how you came up with that number just tell them "I felt it in my bones". It will make every happy.

There is a big difference in the OP and in this situation. In the OP you've instant recognition that the clock did not stop, and instant recognition that that very brief interval between whistle and horn is significant. And you've got quite a lot of additional objective information that all corroborates the elapsed time being only a small fraction of a second.

In your situation, you have additional, unusual activity that required your full attention between the whistle and the recognition that the clock did not stop. You also have a period of time that cannot be reliably estimated any closer than "a few seconds". You have not indicated any "other official information" that would help. So what can you do? Put up 13.1 and go with it. It's what I would do, and what I would argue that any of us should do.

BTW, I have never argued that we should make a "wild guess". I have not suggested we use a "rough estimate". If you have no definite information, you cannot make it up. In most cases, I don't believe we can do any better than the time observed plus/minus an official's count. The OP is a pretty unique situation with a very high probability that a well-informed estimate would be right to within 1/10 of a second.

In my high school science classes I was taught that the result of any calculation is only as precise as the least precise factor used. So if you have two weights, one measured in 10ths of a gram and the other in grams, no matter how certain you are of the first measurement, the result must be rounded to the nearest gram.

So what are we saying when we allow both 1/10 second precision and also nearest second (roughly) accuracy?

What if it were the same situation as above but the "skirmish" took a lot more attention to settle down and before you and your partner knew you heard the horn. Game over?

You put 14.1 on the clock right? Because you had definite information that the skirmishing lasted longer than one second and you saw 13.1 left. You added those two to get 14.1. I don't mean that flippantly, I just am trying to understand how you can say you only had definite information of the 13.1; if they pushed and shoved for a few seconds you could be sure it was at least 1 (maybe even at least 2 --depending on what you had definite knowledge of) and it seems you should give those seconds as well.
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The Sanctuary of Truth Wong Amat

Both or all 3 refs should not be in the middle of the fray. One official should always be standing back observing, which would include the time on clock.

I will add that this year's interps contain "the opposite" play where the clock does not start. The official is directed to take some time off, even though s/he has no direct knowledge of how much time should have been used.

I think we are all concur that looking at the clock simply by one of the officials constitutes enabling the clock to have time awarded to it. But in this situation at the end of a reasonably close game with you and your partner both focussing on the "skirmish more than the clock (which I think my assignor would prefer) let the game end?

All my supervisors say that they want at least one official standing back. If both/all are focusing on that one skirmish then another one could break out undetected, or players could be leaving the bench, etc. But when in Rome....

We had one official watching the 2 players directly involved, one watching the 4 or so that were close to the play and moving in, and one watching the perimeter (and he was opposite, so he would have seen the benches).

That doesn't leave anyone for the clock (at least not right away).

Understandable for the first few seconds. But not for the entire 13+ seconds, IMO.

The kicker is if this all started with 2 or 3 seconds remaining, and the clock ran out. Of course, Bob's crew would have known it was close and taken a glance.

Without being flippant let's say you are working with a newbie like me. You go to break up the skirmish having pre-gamed the situation even and I botch it. I panic. I don't look at the clock and don't do my job with 3 or 4 seconds left the horn sounds. Do we end the game?

If I'm working with a newbie then I will be extra diligent in my clock management. I'm the one who would get the a$$ chewing if we screwed up something like that.

One of the things I'm working on is that it be 2nd nature to glance at the clock every time the whistle blows, regardless what part of the game we are in.

Clock-glancing doesn't come easy
 

I find "clock-glancing" a difficult thing to get into the habit of doing. If my partner blows his whistle for a foul, I am focused on helping him determine if the ball went in the basket, helping him make sure he has both the shooter and the fouler, making sure there's no extra-curricular activity among the players...then the clock. By the time I do all of these things first, I've often neglected to check the clock. I'm afraid if I move "clock-glancing higher on this priority list, I'll miss something else even more important.

Any suggestions for getting into this good habit?