Following on from a customer query, we can confirm that one can install install addressable RGB LEDs/NeoPixels inside a 60 mm diameter arcade button. It’s not the easiest build, so whether one should attempt this is another matter entirely.
Thin (and I mean thin: I used 28 AWG) Silicone Cover Stranded-Core Wire in several colours. You’ll want to cut this quite long at first, as you have to ease it through some tiny holes in the button assembly. If you solder connectors on the end, you won’t be able to disassemble or install the button without cutting them off. Do I speak from experience here? You betcha!
The usual soldering/hot gluing/bending/prying/grabbing/cutting tools you already know and love. In addition, you might consider a non-marring spudger and a pair of arterial forceps (aka hemostats) or needle nose pliers too.
I’m not going to cover soldering the wires to the LED PCB in any depth here. You’ll need three wires: 5 V power, Ground and Data. Even though the LEDs I used need 5 V power, they are quite happy with 3.3 V logic on the data line. They need more than 3.3 V power to light, though.