Just wondering if there is an ohm reading for the coils. I am sure there will be, and that might be worth checking.
I am thinking it is like a "flutter valve" in turbo controller, and the coil energises the shuttle, hence the pumping motion.
If the coil has "faulted" it may be humming but does not have the full "grunt" it needs.

Just a thought from my turbo car ECU tuning days.