Try what I'll be doing to my Cruise (intermittant fault). Run an LED from the solenoid for the fuel cut-off (don't need the starter so the only circut needed for the engine) and leave it at the base of the windscreen, so it's lit when ever the sloenoid it energised. If it goes off and the engine dies then you know it's the imobiliser, if it dies but the LED is still on, then it could be the solenoid.
If you don't want it on all the time, run the LED from the ignition to the solenoid, it will stay off when the ignition is on and the sloenoiod has power to it.