If this is the case, how can we know whether that number represents a drop in population or not? Can we measure population size 100,000 years ago? 50,000? Then compare them? What about that number represented as % of total population? 1,000-10,000 sounds low, but our population probably wasn't very high that long ago either.
Hypothetically if you took a random sample of present humans you would have a low # of say skin tones in wide range, whereas a small isolated and stable population should have a low # of low variety. So you can tell by that kind of difference whether it was a sudden drop or more of a sustained thing. Presumably in a more sophisticated statistical way across a wide variety of genes of course.
Apparently there is another bottleneck ~900K years ago that has decent fossil record support but the Toba one is more disputed.
