I use 2.2mm FASTON-like connectors (top of first image) to connect to the male terminals of the illuminated switch on the left, but they are a pain to connect and sometimes even damage the male terminal.
I found a terminal that is way easier to attach (bottom of first image with blue wire attached) which has a small sheet inside it that acts like a spring and a dent on top to fix the male terminal in place, but I cannot find the name of that terminal. What is the name?
Follow-up: Is there a recommended female terminal type for the male terminals?
The bottom terminal was harvested from a socket that is sold with the buttons (see image 2). But there don't seem to be any sockets for the 12 mm illuminated switches, only the quick connects (also see image 2).