I've said it before, and I'll say it again: spraying thinners through an airbrush fondly imagining that you're cleaning it is only slightly better than trying to shake the paint out.
It's a good start though. Once you have completed your preliminary cleaning , take out the needle, and wipe it down with a thinner soaked cloth. Then fill the cup with thinner and spray through again, but this time cover the orifice (can I say that here?) with a cloth, which forces the solvent back into the cup, dislodging all manner of alarming gunk and detritus that has accumulated in the tip. Repeat until clear. Some use interdental brushes to scrub out any remaining crud, but I finish off with a couple of squirts from a liquid reamer.
Cellulose thinners are the thing to use, and it might be worthwhile giving the tips of your brushes a leisurely soak before trying the deep clean.
Nick