Time Machine "exclude these items..": external hfs+ hard disk greyed out

The problem was, the drive had been formatted / partition mapped as Master Boot Record, instead of GUID Partition Map.

I copied the data to another hard drive, repartitioned / reformatted it as GUID / Mac OS Extended (Journaled), before moving the data back on the drive. Time Machine was then happy to back it up.

Sincere thanks for the replies.

I just ran a quick test:

I have an SSD that's formatted as HFS+ (Mac OS Extended, Journaled), GUID partition map. This allows me to remove it from the "Exclude these items..." list, and TM will back it up.

I suspect the problematic hard drive is using a different partition map, e.g., Master Book Record, which is why TM won't back it up.

The problematic hard drive is at a different location so, I'll check it in the coming days and report back.

Many thanks for your responses.

Thanks P.Phillips. Yes I assume this is the case, but that article only seems to state what format time machine will backup to, not what drive formats it will backup.