I get an error message that my Seagate Backup Plus Ultra Slim Drive cannot be backed up on Time Machine. The Drive is not full and I cannot find evidence of a firmware update on the Seagate website. What else can I do to resulve this issue?

To be clear you want to use your Seagate Backup Plus Ultra Slim Drive as a Time Machine backup device, correct? In other words you are not seeking to back up its contents.

Refer to how to format a disk with Time Machine.

Excerpt:

"If you need to erase the disk manually, use the Disk Utility app to erase using the Mac OS Extended (Journaled) format."

You definitely do not require any particular firmware updates, nor do you require any software "utility" or "manager" products that drive may have included when you bought it. The first thing anyone should do with any external hard disk drive intended as a Time Machine backup device is to erase it in preparation for its use with Time Machine.

Thanks. In that case please read If you can't back up or restore your Mac using Time Machine - Apple Support.