Ever since I started using an airbrush, I have found the most difficult part to clean has been the nozzle.
The best way I found to do that was to take a no-longer-used needle, rough up the point with some sandpaper, pluck some cotton from a Q-Tip cotton bud and wrap it around the point of the needle. Then, dip it in lacquer thinner and gently insert it in the nozzle and twist it. It worked, but was finicky and time consuming.
A week ago, I was watching YouTube videos and one of them dealt with airbrush cleaning presented by Scale Model Workshop. Why this channel has only just over 28,000 subscribers is beyond me. It should be ten times that or more. The videos are very professionally produced by Paul Budzik and full of practical information.
Paul is a dentist, so dental tools and materials make appearances in his videos. In the one I was watching, he showed how he used Absorbent Paper Points to clean airbrush nozzles. Dentists use them to work on root canals.
I checked eBay and found many sellers. I believe the box pictured below was about $6.
After an airbrush session today, I dipped one in lacquer thinner and used it to clean the nozzle, and it did a great job cleaning the nozzle like it was new. Thank you, Scale Model Workshop!