I contributed to this apparently endless string of posts about Time Machine failing in Mojave some time ago. Since then much of the discussion has been well outside my technical competence, but one very useful contribution pointed out that Time Machine is designed to give way to any other data-transferring or -copying applications that may be running.
I use Sync Folders Pro, running all the time, to copy the contents of my Desktop and Documents folders and a folder containing the scores of my musical compositions to my iCloud folder; I also use Carbon Copy Cloner as a backup system in parallel with Time Machine (belts and braces!). After updating to Mojave, I experienced the problem of TM not completing its backup that has been the subject of this string, and therefore abandoned TM for a while; then tried to do a Time Machine backup, but first shut Sync Folders Pro down and ensured that CCC was also not running. The TM backup still did not complete.
Last night I tried TM yet again, having not used it for probably 2 or 3 months, but I first shut down every and all applications that I have set up to start when I start up the computer. TM remained on 'Preparing Backup' for over 3 hours — even though I have a modest hard drive of a mere 479.89 GB capacity — and I feared the worst, but then it started to back up and completely finished the backup in another 2 hours or thereabouts.
So this might be the generally-applicable and technically simple answer to the TM problem: shut down every single running application apart from Time Machine when performing a TM backup.
