I replaced a door lock tumbler in my (long gone) 88 635. This lock was somewhat differently constructed, but the principle was similar.
Someone had buggered the driver side door lock, so I decided to fix it. I got a lock kit from the BMW dealer. It came in a bag that was labeled "not for public sale" but they sold it to me anyway.
In the bag were the various tumbler parts including springs and small slotted wafers (the 635 tumble uses wafers instead of pins). The wafers slid into an array of small slots in the tumbler. They had different lengths of tabs on either side of the slot, and small springs on the sides. When no key was in the tumbler, one side of each wafer stuck out of the slots.
The key was double sided, so when it went in it would move the wafers one way or the other causing the extended wafer tabs to slide into the tumbler some distance based on how the key was cut. I had the key, but had no idea which wafers should go where. So this was basically a trial and error exercise. Put in the wafers, slide the key in, see which, if any wafers retracted properly, Set that wafer aside in a labeled spot, based on which wafers did what, re-arrange them, and try again. It took about 20 minutes to finally get the right wafers in the right spots and in the right orientation. It truly felt magical when I got it right and when the key went in, all of the wafers disappeared into the tumbler.
With the key in the tumbler, I then sld the tumbler into he door latch housing, and connected the back side to hold the tumbler in place.
I do recall that you had to be super careful about holding the assembly or all the wafers and springs woudl fall out and you had to start over.
I am pretty sure the pin version of this used in the E9 is similar...