For that type of spray gun, I just disassemble it, it only takes 5 minutes to pop the front off and clean the needle/nozzle/etc
I have done it the way suggested, spraying varsol/gun wash/etc through until clean and it bit me before in the form of orange peel in the finish. I tried everything and couldn't get the orange peel to disappear, took apart the gun and found a spec on the needle (or maybe the nozzle), cleaned it properly (disassemble) orange peel gone. Lesson learned, I just take it apart every time.