How to disable "ignore ownership" option on an external volume on Mac OS X El Capitan?

Solution 1:

From comments, your disk is formatted as FAT32, which is incapable of holding unix or even Windows permissions.

It is also very dubious in its hardlink capability. You can force them, but file repair tools are likely to break them.

By far the best format for Mac backups is GUID/HFS+ not MBR/FAT32.
You will need to Erase (not Partition) the entire disk to change it to GUID/HFS+ (macOS Extended, Journaled; GUID Partition Map in Disk Utility) so you will either need to abandon your first effort or back it up somewhere - but note it will not have correct perms already, so I'd suggest starting over.