Probably a more robust test would be asking the caller to run their hand through their hair a few times. Maybe you could pre-render a few samples, but it would be trivial to request the person pass their hands through their hair in a specific way, or simply do it again after their hair is already messed up a bit from the first time. It could still be defeated by the caller having the same hair style (or wearing a goo…
That would have trouble passing anti-discrimination requirements: disability (no hands), medical (bandanna covering cancer treatment hair loss), religious (burka, rasta, yarmulke, sheitel), racist (cornrow).
And trouble with: dreadlocks (can’t run fingers through), bald headed guys (as mentioned by sibling comment), and people with hairdo’s (coiffure, hairspray, topknots, plaits etcetera).