Well, if the ECT sensor is faulty, it will confuses the ECU and when my ECT sensor went kaboom, my idling was rough and sometimes shoot
up to 2000 rpm as well but not constantly, most of the time the idling would drop so low and cause the engine to stall.
Do you see any black smoke coming out of your exaust while idling or before the car stall???, Check the spark plugs as well