This still does not make sense. The 60A alternator excite wire is switched from the ignition switch. It would not have 24 volts with the ignition switch off.
Evidently, it's not controlled by the SRS switch when it's connected directly to a 456 wire, of which there can be multiples. The 456 wires are apparently getting the 24V that also goes to the TSU, Fuel Cutoff, Glow Plugs, Cold Advance Switch, to name a few. When the 568 wire is connected directly to the 456 wire, the 24v supplied through the 456 takes the place of the voltage normally supplied by the excite wire, or so it seems. I can't adequately express what's happening. All I know is that with those two wires connected, the fuel cutoff was not being controlled by the SRS switch and the truck kept running. So far, with those two wires not connected and tied off, the truck is shutting down every time the SRS switch is turned to the STOP position.