Can't back up to 3rd party disk using time machine

Hello drmarkf,

Thanks for reaching out to Apple Support Communities. We see you have some questions about backing your Mac up with an external drive, and we'd like to help. The following link may be able to help, as it explains how to back up using an external hard drive, with Time Machine: Back up your Mac with Time Machine

Select your storage device in Time Machine settings

When you connect the storage device to your Mac, your Mac might ask if you want to use it for Time Machine backups. If it doesn't ask, follow these steps.

1. Open Time Machine settings:

* macOS Ventura or later: Choose Apple menu  > System Settings, click General in the sidebar, then click Time Machine on the right.

* Earlier versions of macOS: Choose Apple menu  > System Preferences, then click Time Machine.

4. In Time Machine settings, select your external storage device as your backup destination:

* macOS Ventura or later: Click the add button (+), then follow the onscreen instructions.

* Earlier versions of macOS: Click Select Backup Disk, then follow the onscreen instructions. 

7. If the storage device contains Time Machine backups from another Mac, you might be asked to claim the existing backups so that they become part of the backups for this Mac. Or you can choose to start a new backup instead.

Let us know if this helps.

Regards.