I find that just spraying cleaner through the Aztec nozzle or even soaking it (detached from the airbrush!) doesn't completely clean it and the needle tends to jam full forward eventually, which means it won't spray. Taking the nozzle apart isn't that big a deal. There are basically three parts that I'll call the shell, the liner, and the needle/spring as shown below between the assembled nozzle and the microbrush:
Disassembly - Pull on the exposed part of the liner and it will pop out of the shell. Then pull on the base of the needle and it will come out of the liner. Clean the parts with windex (acrylic) or lacquer thinner/mineral spirits (enamel) using a microbrush.
Assembly - The needle/spring goes into the liner and that subassembly goes into the shell. The needle/spring just slides into the liner and appears to self align. That subassembly has to be rotated slightly (indexed) within the shell while they're being pushed together until it seems to click into place. I recommend that you push the subassembly in by holding the liner so the needle isn't pushed forward during final assembly. After assembly, the subassembly may be a little wobbly within the shell; the needle/spring should be easy to push in and then spring back on its own.
If the nozzle isn't spraying, step one is to take the nozzle off and look at its base. If the bottom of the needle (the plunger sticking out of the bottom of the nozzle) is stuck forward (you should be able to push it in and it springs back; instead it will be flush with the base of the liner), then coax it out with the tip of an xacto blade - if the insides aren't too dirty, it should pop back into the normal static position as shown above. Then check it by pushing it in to see if it springs back. If it jams forward on that check or doesn't push in easily, take the nozzle apart and clean it. If it seems to be working okay but jams again when put back on the brush, take it off and apart and clean it. If you can't get it to easily pop back into the static position when you first take it off the airbrush, then take the nozzle apart and clean it - you'll undoubtedly see why it needs it.
The red and orange nozzles have a "plastic" rather than metal needle, a slightly different bottom on the needle, and some spring is exposed when fully assembled. The disassembly/assembly is the same, however.