Time Machine monitoring app using data from the "tmutil status" command
Solution 1:
I have made a shell script to output of 'BackupPhase' from tmutil status
to the menu bar, and then I have the rest of the information available if you click on the menu bar item.
To display the output of this script in the menu bar, you will need the excellent TextBar app, which costs $5 (IIRC) and is well worth it.
Here's what it looks like right now (the "ThinningPostBackup" part is what is shown in the menu bar. The rest only appears when the menu bar item is clicked.)
You'll notice the top 3 sections are formatted, and then I just include all of the tmutil status
information below (everything from "Backup session status" and below), because sometimes it might have interesting stuff in it, and I'm nerdy like that.
I have put my TextBar / Time Machine script up on GitHub for anyone who would like to use or adapt it.