Well when you bypass the injector with the noid light, then you are removing the injector completely from the system.
I would look for mouse trails (droppings, food etc) The wiring is local to under the hood, from the box with the ecm down along the frame rail front edge then up by the transmission, then across the top of the injector rail. Look for where a mouse might have chewed through the wire. If you do not find such a place, the next step is pretty invasive and would require either getting an ecm out of a salvage yard, or performing a wiring overhaul at the ecm.
Just to let you know, all the injectors should have a full 12v.... they pulse with a variable ground.... the ECM provides that variable ground. So if you have a wire from injector number 3 that is.....shorted to ground then you would have a light on steady.