Unable to mount Seagate drive for Time Machine backup on iMac

Can you get the SMART status?

Open “Disk Utility” on the Mac, Disk Utility is found in the /Applications/Utilities/ folder

Select the disk from the list at the left of the Disk Utility screen (select the actual main disk, not a partition)*

Look for the “S.M.A.R.T. Status” of the disk information overview in Disk Utility

Frankly, hard drives don't last forever, and some may not last all that long at all. This is why you need to make multiple backups.

Can you reformat the drive completely with Disk Utility? Of course all your backup will be lost but this will tell you if the drive is even slightly capable of doing things.

If Disk Utility cannot even mount the disk, you're pretty much stuck.

Try a different cable. Try a different power supply (assuming the drive uses one). Try booting Recovery and using its version of Disk Utility. Try repeatedly smacking the drive with a blunt object (no joke, I did that with a TM backup drive about a decade ago and it remains in service to this day).

If all else fails the disk is dead. Throw it away. You did choose to encrypt those backups, right?

John Galt wrote:

Try repeatedly smacking the drive with a blunt object (no joke, I did that with a TM backup drive about a decade ago and it remains in service to this day).

Story time:

I remember 20 years ago I had a drive with "sticktion". Banging it did not good. I needed to get the drive up and running again only once (back in those days backups were sporadic). I told people how I had opened the drive and gave the platter a small push which got it moving. They were horrified! You NEVER opened a drive! I repeated I only needed to get it running one more time to copy the data. In fact the drive did boot up and I copied the data. I was even able to put the cover back on and use it for a while longer, though of course I didn't trust it anymore and once I had a new drive I replaced it.