How long after fuel stops flowing before the engine quits?

Well, in that case, you should, at least once, select OFF while it is running at idle to get a feel for how long it takes to start complaining.
If you can get it started and taxi to the hold line quicker than it runs out of fuel, you might want to slow down the first launch of the day.
The time it takes to start to lean out would be the same amount of time that a bad tank of fuel/water would take to reach the carbs.
If it runs without issue for longer than your reference starvation time,  you can feel confident that the probability of a fuel issue on departure would be minimal.
If it was going to stumble because of fuel starvation, it would have already happened.

It just occurred to me that this thread has come full circle.
Your title of, “How long after fuel stops flowing before the engine quits?” Is Not a question that you should be asking,
but a question you should be answering.

This is a question that every pilot should have the answer to.
The answer is simple to determine, select OFF and start timing! "

Bill Hertzel wrote:

It just occurred to me that this thread has come full circle.
Your title of, “How long after fuel stops flowing before the engine quits?” Is Not a question that you should be asking,
but a question you should be answering.

This is a question that every pilot should have the answer to.
The answer is simple to determine, select OFF and start timing! "

I did want to but my instructor said that it would dry out the carbs and we'd have to open it and refill them, so we didn't.

You can run out the fuel for the purpose of the experiment.

After reopening the Selector Valve, gravity will refill the carbs within a minute if you have high tanks.
The AUX pump will refill them in 10 second if you have low tanks.

If you are not going to use the plane for longer than it takes for the carbs to dry out by evaporation (Weeks?), Selecting OFF may be the better choice.
Drying out the Carbs once may be better than continously refilling the bowls and evaporating the lighter fuel components continuously to the point that the fuel is slowly "distilled" down to a resinous syrup.
- - -
Engines need to be operated on a continuous basis.
The worst thing you can do to an engine is to run it without OIL.
The Second worst thing you can do, is to not run it al all.