Unable to include external media drive in time machine backup
Best guess is the drive is the wrong format.
Time Machine won't back up NTFS, FAT or ExFAT.
APFS should work, but 'safest' is HFS+ [MacOS Extended, Journaled] using GUID, not MBR. These options are available in Disk Utility.
You will not be able to change the format &quot;live,&quot; you will need to copy this data elsewhere, then erase the drive &amp; then copy back to it afterwards.