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The cat/var/system.log seemed to work for me

I tried running the disk utility, and that didn't work for me.
I tried re-selecting the external drive, and that didn't work.
I went to the terminal and found an error and excluded that file. I haven't gotten an error, but has been in "cleaning up" for some time.

How long does "cleaning up" take?

Yeah! It finished. Guess I need to be more patient.
 
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Another solution which usually works for me is to boot into Safe Mode, but I have no idea why. I read that tip years ago. It doesn't always solve the problem at hand, but it does solve many of them!
 
I seldom complain about my Macs and how they perform. However, since upgrading to Mojave, I have been experiencing constant Time Machine backup failures, whether to my Time Capsule, external HDD and even a brand new 1TB Crucial SSD. All were reformatted HFS+ Journaled. Still no luck. Changing the format of the drive to MacOS Extended (Case Sensitive, Journaled) has worked for me. Three Macs have now successfully backed from scratch up on the external HDD as well as the Time Capsule.
 
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