My first thought was an alternator problem keeping ignition circuit powered up, but that can't be the case if you can flip the fuel switch to the center position and engine will die. What happens when you flip that switch to center position is it turns off fuel flow to fuel pump via a solenoid valve in fuel line. Engine runs until carb runs out of fuel. Alternator ign terminal, fuel pump shut off solenoid, anti diesel solenoid, and choke are kinda on the same circuit.
I think the next thing I would try, with engine running, would be pull the yellow wire connected to terminal 86 on R18 and R19 ignition relays in lower control box. If engine dies, go back through the wiring to determine why that circuit remains powered when ignition switch is off.
If engine continues running when you pull the wire connected to 86 on R18 and R19, you either have a stuck relay or something is wired up wrong.