It would be nice if ExifTool could accept null time values as 00:00:00 instead of rejecting them, when updating Metadata
But it will:
> exiftool a.jpg -datetimeoriginal='0000:00:00 00:00:00'
1 image files updated
> exiftool a.jpg -datetimeoriginal
Date/Time Original : 0000:00:00 00:00:00
However, from your other thread (https://exiftool.org/forum/index.php?topic=7620) I think you may be trying to write filesystem timestamps, for which time zero depends on the epoch of the filesystem.
- Phil