Engine immobiliser/alarm light faiils to illuminate solid or flash

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I have a Cougar V6

The Engine immobiliser/alarm light fails to illuminate solid or flash ..

Under normal operating conditions it will go solid when the ignition key is turned one position prior to starting the engine or will go solid then flashes when engine is turned off .

However after driving the car the condition normalises but returns when the engine is cold.

Fuses and relays have been checked .

Can any one help ?

Thank-you