Dave, you may be right though I've not heard of this. Both my cars have hiline packs so I can't check. The workshop manual doesn't say anything other than the starter is disabled, and messages on the hiline. There isn't a separate lamp on the lo-line pack from what I can see.
EDIT: I've found another section that says there is NO visible or audible indication of the immobiliser system status unless you have a highline pack when you get the 'engine disabled' message. So that suggests the flashing of the instruments is some kind of fault. It could be an earthing problem as I reckon the Immobiliser shares an earth with the rest of the dash. Also, the immobiliser cannot cut power to the instruments or other systems. It can only prevent the starter motor from operating, and tell the engine ECU (Engine Control Unit)
not to allow the engine to start.
It is also possible you have a faulty starter motor / solenoid, or possibly the relay in the immobiliser ECU
. I have only come across the faulty relay once, the starter solenoid is much more common especially on diesels.