Again form memory, the shut off solenoid should be a three wire. One ground, one pull in circuit(high current) and one hold in circuit (lower current). Used to be red,black and white. The pull in coil activates with the key switch once the parameters are met and pulls the pin in on the solenoid letting the plunger in the injection pump move back due to spring pressure.
There is a timer circuit that shuts off the relay for the pull in coil after a few seconds. The hold in circuit should be activated and holding in the solenoid via a relay on the third wire. (Low current draw)This will stay held in until the key is cutoff,a safety switch/engine protection switch is opened or the hold in relay opens up for some reason.(like a bad relay getting hot).
Like I said this is from memory on this model from around 2012. So it may have changed.
Hope that helps.
This agrees with what was posted prior and tested earlier. I installed a light bulb on the hood and wired it to the ground and hold in circuit, and watched the light as it was dying. Never did the light ever flicker or go out as the engine died, and only went out when I turned the ignition off.