I know that I’ve learned from other TD’s who have shared situations online, so here is my contribution. The following scenarios are based on real games from the IL Class Championship. The time control is G/60 with 5 second increment. What would you do?
Scenario 1: In time pressure, there is bishop-knight vs. lone king endgame in the class B section. Both players have quit keeping score and it’s obvious the “winning” player doesn’t know how to finish. A TD is present and observes 100+ moves but neither player requests help. It’s the last game still going on in the round.
Scenario 2: One player runs out of time but his opponent doesn’t realize the flag is down. They continue to play and the player who has flagged quits hitting his clock (probably why he flagged to begin with). As a result, the opponent’s time never goes down. The player with time should win but it’s an U1200 section so stalemate is also a possibility. It’s the final round of the tournament and the game impacts 1st - 3rd place trophies.
In other words, the lack of response to your original question is: there’s no good answer.
According to the rulebook, you can’t call flag fall. You can’t even declare the game a draw. If you waited until both flags fell, you could call a draw. (Rule 19J maybe?) However, as it is, according to the rulebook, there’s nothing to do.
Here’s what I would do. The rulebook allows a generic “if it isn’t covered in the rulebook, do something that makes sense and is consistent with the rules that are covered in the rulebook.” Based on that, I would tell the players, “Gentlemen, the next round (or trophy ceremony) needs to start. If this game is not over in (5 minutes? 2 minutes?) I am declaring it a draw.” In the case of the Bishop Knight endgame, a draw is the appropriate result anyway.
In the case of the flag fall, it will probably prompt the kid to actually look at the clock and notice the flag fall, and he’ll declare it. If it doesn’t, then it deserves to be a draw anyway. Clock observation is part of the game.
In one Chicago Class (well, maybe it was a Midwest Class) there was a game in the expert section with K+Q+5seconds vs K+Q+P+3seconds. The other sections were already paired and ready to start while that one game was still going on using delay time. After going for more than 150 moves (with the pawn stationary) the player with the K+Q said something like “is there any way to end this” which the NTD floor chief immediately treated as a draw claim and awarded the draw.
In one G/30 scholastic event with a pair of very-low-rated 1st or 2nd graders were using and both punching an analog clock, the player that had flagged had a much better position while the other player was moving quickly and still had 15 minutes left (which would probably not run out for another hour). I asked both players what result they were trying to get and both were trying to win (the player with the inferior position added a comment that made me realize that he thought that the clock had to go all the way around again before the flag could be called). I then went outside of the tournament room to find and talk to the parents of both players, letting them know what was going on and that I wanted to simply declare it a draw as a reasonable compromise between the flagged person having a much better position and the other player not realizing the flag was just waiting to be called. The parents agreed and that ended that game.
In the final round with trophies affected like that, the reasonable option I chose would not be a particularly good one for you.
In one Chicago Open I saw a player flag in the first time control with the clock then proceeding to the second time control (Gametimer with the red flashing light showing that the first control was not reached on time). The opponent did not realize that he could call the flag and eventually (about an hour later) both players reached the time control and the flashing light went off.
That’s actually similar to what happened here. I was getting ready to have the other TD get pairings ready as if it were a draw (so that we’d be ready to go) when the player with the lone king made eye contact and half-shrugged.