Thanks Muguy.
I have a problem: My Time machine backups appear to be inaccessible, and the backups haven't been working since 1st April (unfortunately, it doesn't appear to be a practical joke), and YES I should have looked into it there and then but have had other very important pressing issues to deal with before and since; it's ext seagate 2TB USB drive now appears to be reluctant to mount. I have successfully erased a 1TB Fanxiang USB flash drive with the hope of using for backing up the iMac, but when attempting to Restore from the macintosh HD or even Macintosh HD Data I always get a failure message in the sequence:
Validating target...
Validating Source...
Repartitioning target device...
Could not change the partition type for /dev/disk4s1 - error - 5342
The operation couldn't becompleted. (OSStatus error - 5342.)
Operation failed...
I have tried selecting as source variously the drive (USB flash) or the volume on it, whichever is offered for selection for the Erase op (always successful), and for the Restore op(always fails.) and repeated the processes many times.
I don't presently have another drive large enough to accommodate an initial backup, but have attempted both an Erase and Restore on a 64GB, with exactly the same outcome/results as for the 1TB USB Flash.
Any expert advice would be extremely welcome please.
Best wishes