I don't break mine down between colors as you can introduce water or whatever solvent you are using. Between colors I clean the color cup and run water through my airbrush till its clear.
When I'm done with my airbrush, I run water through it (I use water based paints). Once I believe its clean, I take the needle out and using a small squeeze bottle run water and some window cleaner through the hole where the needle goes in. I flush with water. I then clean the tip and needle.
I reinstall the needle and run more water through the airbrush. When there is no more color of any sort, I just blow air through the brush. After that I have a lube I got from Bear-Air and put a couple of drops on the needle.
This has worked great for me as I still have the same Paasche VL I bought some 13+ years ago.....