I don't see how it could be the pilot bearing because the input shaft and the flywheel/pilot bearing are turning together when the clutch is not engaged.
It could however be the throwout bearing. I have heard such sounds in the past on other vehicles. The sound goes away when the bearing is loaded up by stepping on the clutch. It could be caused by just a light pressure on the throwout bearing. Try adjusting the slave cylinder or clutch pedal so that there is more freedom for the throwout bearing.
Did you put in a new throwout bearing?

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1977 300d 70k--sold 08
1985 300TD 185k+
1984 307d 126k--sold 8/03
1985 409d 65k--sold 06
1984 300SD 315k--daughter's car
1979 300SD 122k--sold 2/11
1999 Fuso FG Expedition Camper
1993 GMC Sierra 6.5 TD 4x4
1982 Bluebird Wanderlodge CAT 3208--Sold 2/13