How to include an external USB HDD to be backed up by Time Machine?

iMac (Retina 5K, 27-inch, 2017)

MacOS Monterey 12.7.6

External USB drive formatted HFS+ Journaled, mounted

Time Machine back up volume: Ugreen DXP4800 NAS

I am able to back up my Macintosh HD to the NAS. But I want to include my (permanently attached) external USB drive's contents as part of the Time Machine back ups too. How do I do that? The external USB drive is mounted and it does not show up in the excluded items. So it's not that it's been excluded accidentally or anything. It does not show up when I click on the Time Machine options. How do I manually include the USB drive to the backups?