I would disassemble it and soak it in laquer thinner overnight. Take the air valve out and do NOT soak that in laquer thinner. There is an o-ring in it that might be ruined.
If you can get some good pressure from your compressor, after it has soaked blow out the air passages thoroughly with compressed air.
Also, make sure the head is tight. Not just finger tight, but pretty solid. Before you store the airbrush loosen the head. That will prevent that Teflon washer from getting flattened so quickly. In most cases that washer not sealing properly is what causes pulsations in the airflow.