Anecdote - one time I discovered it was the keys in my pocket that made a noise at a certain pedal position.
Question:
Only the hardest four gears? Meaning smallest four cogs and only in the big ring? All other gears are silent? And shifting is all smooth and precise throughout the range?
If so, that has got to be a derailleur/cable thing.
And when the left pedal is at 12 o'clock, the right pedal is at 6 - so check down there too.