BMS noob question

Will a 13s BMS work on a 12s pack leaving the last balance wire off ?
Or do they only work for the stated number of cells ?

depends on the BMS, in general no.
Leaving one wire off will definitely not work. Normally you either put them on GND or short them somewhere.
But if it’s not a dirty cheap china BMS, there will be a datasheet with instructions how to use it.
Most “real” BMS use a TI or LTC chip for cell monitoring which can be configured for a wide range of cell counts, usually from 5-16S. But for configuring you also need a datasheet.