Should see squirt of fuel from A pump. If not A pump faulty, circuit plugged, pump plunger stuck or steel welch on face of carb(not the brass dust cover) leaks.
Mostly likely plugged circuit.
Treemonkey has stated publicly that it's not the accel pump, I take him at his word.
I've leak tested and traced every passage and have found no blockage. Both bad carbs are in excellent condition, appear to be almost new, they both came on low hour, very clean 359's with scored pistons. The good one came on a 357xp from a tree service that looks quite well used.
If the saw is a low hour sit on a shelf more time than not saw chances are the brass plunger is not worn out. Clean and check for leaks. O-ring may still be suspect.
Of course I checked the accel pump circuits anyway, mine have black plungers with a double lipped seal like an x ring, all three show no obvious wear and pump fine.