IIRC, there's a passage off the float bowl that supplies the accelerator pump diaphragm chamber thru a one-way check valve. Gravity keeps that chamber full, just like the bowls.
When the accelerator pump rod is pressed by the throttle linkage, the diaphragm causes fuel to squirt up into the little opening in the throttle throat. Typically, there is a pipe that spans the gap between the two carbs so that the one pump feeds both squirters. If you completely dismantle the carbs, all that volume can take a bit of time / pumping action to fill.
But, you're on the right track as far as using carb cleaner spray and/or compressed air to blow 'em out. If you have an air nozzle with a rubber tip, you can press it hard and feel the air blowing out the tiny nozzle with the tip of a finger.
On the other hand, I'm not convinced that that's your trouble. The accelerator pump only activates when you open the throttle. At the steady-state tooling around that you're describing, the accelerator pump is not really moving.
Under load, that might be a different story, but even then, if you open the throttle under a load and the AP is not working, EVENTUALLY, the carbs catch up and supply the proper fuel. The AP was just an add-on in an attempt to eliminate the hesitation that would otherwise develop. The way you're describing it, you're not experiencing an HESITATION as much as a complete lack...
As for timing, are you sure that the pulse generator isn't mounted on a mechanical advancer mechanism? In the early days of point-less ignitions, the spark was indeed generated electronically, but the ADVANCE function was still handled mechanically. It was only later that the advance function went electronic as well. I guess it would depend on the exact year of your bike. And I could be wrong for that model anyway. It could be that they came along AFTER the migration to full-electronic.
Just a thought...
Kirk