Cannot Mount Time Machine

Startup in macOS Recovery, open Disk Utility and see if it can Repair the Time Machine partition.

As a side note, it is not a good idea to partition your TM drive and use it for other things. Personally I think that I would get a new external drive to use solely for TM and then decide on what to do with that drive.

The other 1Tb on my 2Tb External drive is partitioned into 4 separate partitions, these being 200 Gb for my work folders, 200 Gb for my Account files, 549.65 Gb for my various iPod back-ups and 49.87 Gb for any Spare files

If that drive fails how do you plan on recovering the files in those other partitions?

Here's some food for thought:

Get another 1TB EHD and copy the each of the 4 volumes into a folder of the same name on the new EHD.

Next, erase each of the 4 volumes on the TM drive. Try to repartition the TM drive so that the TM volume is the only volume on the drive and has full capacity. If you can't do that and are sure you have all the files you need on your Mac and the new EHD, erase the TM drive to one volume and start over with a new backup of both your boot drive and the new EHD.

What is on the other 1T partition and does it mount?

Unfortunately you will not be able to copy the TM backups if you can not see or mount them.

I always keep at least 2 or more backups on different external drives. In addition to Time Machine I also use CarbonCopyCloner to make weekly and monthly clones on 2 other drives.

Plus I would never ever make a habit of deleting stuff and then relying totally on Time Machine to get it back.

FWIW, it's probably greyed out because Time Machine is still enabled. Try turning off Time Machine in System Preferences. The other thing I would mention, you don't have to run Disk Utility from Recovery Mode on external drives.

dialabrain wrote:

FWIW, it's probably greyed out because Time Machine is still enabled. Try turning off Time Machine in System Preferences.

It's more than likely grayed out because something is wrong with the drive or the enclosure. ON or Off in TM Pref. shouldn't matter, a TM drive should mount in Disk Utility the same as any other drive.

The other thing I would mention, you don't have to run Disk Utility from Recovery Mode on external drives.

True, I only suggested that to explore a couple of different angles.

den.thed wrote:

It's more than likely grayed out because something is wrong with the drive or the enclosure. ON or Off in TM Pref. shouldn't matter, a TM drive should mount in Disk Utility the same as any other drive.

Unless of course it's on a separate partition

True, I only suggested that to explore a couple of different angles.

What was the other angle?

dialabrain wrote:

Unless of course it's on a separate partition

I don't follow you, all partitions show up in disk utility.

What was the other angle?

A restart and remount of all drives and the partitions on those drives.

Now I'm kind of wondering if are you here to actually help the OP (acprinting) or to just judge the other helpers?

den.thed wrote:

Now I'm kind of wondering if are you here to actually help the OP (acprinting) or to just judge the other helpers?

I just try make sure users aren't directed to try unnecessary and pointless suggestions. Such as…

"A restart and remount of all drives and the partitions on those drives." when they are only having an issue with one.

Or testing external drives from Recovery Mode, etc.

At this point, I think I'm done helping.

acprinting wrote:

Thank you again den.thed,

You're welcome.

The other 1Tb on my 2Tb External drive is partitioned into 4 separate partitions, these being 200 Gb for my work folders, 200 Gb for my Account files, 549.65 Gb for my various iPod back-ups and 49.87 Gb for any Spare files. All of these other Partitions Mount okay on my iMac and their names are in Black type under my Disk Utility, Finder and Desktop screens. However the Time Machine Partition is greyed out in Disk Utility and does not appear at all in Finder or on my Desktop (although it has done in the past).

That is strange.

I appreciate your further helpful suggestion regarding carrying out additional Back-ups and would add that I do not rely on my Time Machine for my Back-up files and only noticed the problem with Time Machine, when I was aware that my iMac was performing slower than usual and wanted to use Time Machine to revert to an earlier version of my system that performed faster.

Hmm... while I've had TM kill a drive in the past, I have never had TM mixed with other partitions on a drive. Yea good idea, if I'm looking for an old file or app. I generally turn to one of my clone drives.

What earlier version were you thinking of returning to? If you upgraded to say Catalina, then that could have caused a major issue for those old Time Machine backups and why you can no longer see or access them.

More info is required in order to proceed. For example: what macOS made those TM backup and what version are you currently running? It may be possible to down-grade to the previous macOS and and then recover from those earlier TM backups. However there is a great risk of loosing everything if you do not have a current backup of everything in the existing macOS. Then sadly the catch 22 is that, the backup of the current macOS will not work in with the earlier macOS.

In closing I would reiterate my thanks to you for your help in this matter and it seems that I am unable to transfer my (greyed out) Time Machine files to my new separate External Drive.

Again you're welcome. At this point I think that I would get a couple of external drives. 1 to move the files on the other partitions to and one to backup the current macOS, before trying to do a down-grade or earlier macOS reinstall.