1988 Ford LTD Crown Vic no spark

In the last 2 weeks our car has an intermittent problem of not starting. I have traced it down to no spark. I have changed the rotor and distributor
cap. I have replaced the spark module with a used one. Once the car sits for a while it will start and run good. When you shut it off after its warm it will not start. Its a 5.8L with 205000km. I am wondering about the pickup coil?

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