We say "on the spectrum" because the spectrum is like a linear map, and your place on the spectrum is like where you put your pin "on the map". Like where you place an icon "on your screen". On is very physical. We could potentially say "within the spectrum" but that sounds more like the spectrum is a restrictive boundary - we want it to feel more like a map - a reference on a wall, not a cage that contains.

on the road on a trantrum on one's own on a whim on a trip on the way on short notice, (idiomatic expressions)