I know things... A lot of things.
Join Date: Feb 2015
Motorcycle: GSXR 750 K4
Re: what fires secondary injectors?
Again, you don't mention how you measure continuity exactly. If you probe the same gray wire at the injector connector and at the ECU connector, with the DMM in continuity mode (beeper mode) and you don't get a beep on the working injectors, then I don't see how they can be working, as the wiring between injector and ECU must be severed. So I don't think that's how you measure it, which begs the question: where on the circuit do you put the DMM's needles?
Regarding your confusion about the 12V: like any device, the injector needs a voltage difference applied on it to do work, i.e. it needs to be connected with a wire at 12V and another at ground. The way this works here, is that the injector is permanently connected to +12V and its ground lead goes to the ECU. When the ECU wants to energize the injector, it temporarily (internally) connects its ground lead to ground. When it wants to turn it off, it "floats" the ground lead, i.e. connects it nowhere.
I have a feeling your non-working injectors might be permanently grounded, due to some wiring fault. Do you get a flashing FI on the dash?