Using WD My Passport External HD to backup with Time Machine

I suspect your internal HD got listed among disks TM can use. In the opening TM pref pane click "Select Disk":

On my Mojave install that shows this, just my backup disk:

See if Macintosh HD is listed there under "backup disks" and, if so, highlight it and click "Remove Disk." Then it should not show up as excluded, or at least be removable from the exclusion list.

Adding something to the exclude list means it will not be backed up by Time Machine. You want the external drive on that list, because you don't want to back up the backup disk (sort of a tautology, right?).

Not being on the list means it's included. The idea behind that list is if there are folders you do not want backed up, you can add them. If the list is empty except for external drives (which is the default), then your entire drive will be backed up, which is probably what you want.

You've added your internal drive to the exclusions list, which means TM won't back that up, either. Select Macintosh HD then click (–) at the bottom of the list, and you're good to go with TM backups. The TM icon on the external drive means it's properly set up as a backup disk.