Since starting this thread on Sep 30th I have followed it quite carefully and I believe the summary of findings from users including myself is as follows -
1. The Time Machine backup problem began with 10.14.0, was never patched by Apple and seems not to have been addressed in 10.14.1. Apple support have denied any problem and have issued no useful advice (that I am aware of).
2. The workaround for most if not all users has been to format the backup drive using MacOS Extended Journaled Case Sensitive. This was not required pre 10.14 and no confirmation or explanation has been given by Apple as to why it is now necessary, but it does seem to be the basis of at least a temporary solution.
3. If you are using, or have used, "App Cleaner & Uninstaller" this may well be the source of an additional problem. But the app developer has described the problem and the fix and this can be found documented earlier in this thread.
4. Some users, like myself, decided early on that because of the obvious broken code in Time M it would be better to use a 3rd party backup app, at least until Apple issue a properly tested fix. So I use SuperDuper from Shirt-Pocket.com which was suggested by other users as can be seen early on in this tread. It's a solid product and more than does the job and I can recommend it.
5. While following this thread I have tested Time M on 10.14.0 and 10.14.1 with the backup disk formatted with the "case sensitive" option, and in my case as well as for many others this, along with fixing the "App Cleaner & Uninstaller" problem seems to provide a workaround and temporary solution. There is of course no guarantee that it will work for all users - but its worth a try.
