Get under the car and listen/feel around the bell housing area.
That really does sound like a flywheel bolt touching the disc and matches with the randomness of its presence. Ive had it happen and at times it was a light tick or nothing and then it would start sounding like a hammer on roids. It was a easy fix and surprisingly no damage done to either the bolt or disc.
i also found the noise to differ when pressing in the clutch, it be quieter when the clutch was pressed in.
Id say if the sound goes away when you put oil in it is most definitely lifter or rocker related-id change all that shit as you may have one that is fubar without knowing it.Before you do all that check all you gaps with proper feeler guages to enure its just not needing to be shimmed-good luck man-hopefully its not a bent valve-is there abnormal exhaust smoke or is it running a bit off-compression test the cylinders you might find a valve isnt sealing properly