Try giving the stick a waggle if this issue occurs. It might not cure it permanently but it will show you where to look at least. Intermittent faults are a pig to trace. It might come up on a fault reader check as some things don’t bring a warning light/flag on.
If it is the Start Inhibit relay, that is part of the IVM Supply Module. If it will start in Neutral but not Park, that might be a clue too. Worth a check.
If the solenoid goes over (you will need to listen under the bonnet for the ‘click’) the it isn’t the inhibitor. There should be volts on the solenoid when the key is turned. No volts means the inhibit switch is active, or there’s an electrical issue.
Given it will start, that suggest the battery is OK. The faulty starter issue causes a massive voltage drop so usually causes all the lights to dim, but it doesn’t sound like that is happening, so solenoid as suggested above is worth a look. No idea where it in a V8. I only had lowly IL6 oil burners
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