Your supplier doesn't have the information (or a name)? That would be specific to what you have.
Your pics are too much surroundings and not enough bms- if it has 2 layers it's hidden well, and the cell connections are in that hidden bit.
Guessing could lead to problems or damage.
Google search 'wiring a 16 cell bms', click on the images link- there's loads of wiring diagrams and pictures here.
You should get 8S BMS for 24 V pack (or modify existing one - though it's not an easiest job) ...
However, I don't really think, that serial connection of 2 BMSs is the best idea ...
I think he wants a 48v and 24v 20 ah combined and charge at 48 and 24 just to play with. It works best if cells are match. So maybe used at 14ah ( guess ). Get a 8s bms. Plus more info.
if he tries to use it as two packs for 24V and 48V then he needs to buy a 24V charger and a 24V BMS so it would be the same cost to just buy a 24S BMS and 72V charger.
if his controller is not built for 100V then he has to buy a new controller to use the 24 and 48V packs in series also.
if he uses the current BMS and the packs are rebuilt to make them all in parallel at 16S then he can use the same 16S BMS and the same charger and the same controller. so that was why i asked why he would decide to make it so much more cost for no reason. and on top of it he has the risk of damaging the pack if he decides he can do it with no BMS on the 8S. he still has to buy the 24V charger though even if he skips the 8S BMS.