PATS - Starter Issues?

[DFHcomputer]

2000 Ford Explorer LTD, V6 SOHC - replaced starter and solenoid, new battery, new fuel pump.....and she starts 95% of the time and runs like a dream. I bought this car used, with one key and remote locking fob. On occasion however, turn the key, all lights etc work fine, but no starter. Hear the relay click etc..... Leave it a while, come back and she fires up just fine. I'm seeing other posts talking about the PATS - any useful diagnostic hints to find out what the issue might be? Any ideas? It's almost as if there's a timed 'reset' on the starter..... starts great from cold; it's the 'quick trip' starts it doesn't like - (run in gas station, grab coffee, come out, no starter action..... sit and drink coffee for 5-10 mins, starts up fine with no problems...) - VERY frustrating! Anyone suffered anything similar?

 

[DFHcomputer]

More info....

according to http://www.blee1099.com/pats_job_aid.pdf - my model doesn't have a starter interrupt - so I guess it's not a PATS issue - what else can I try? I've also just noticed, that even with the key in the 'on' position, I can't shift into Neutral to try and start her that way.... could that be an issue - transmission position sensor or something? I've also seen threads talking about key actuators in the steering column..... all suggestions gratefully received....