Silly me.
I said before I edited the mosquitto.log file.
Seems I didn't.
sudo nano mosquitto.log
Though it mentioned the file had been written to while I was editing it: "Do you want to write to file" and I said YES.....
It wasn't done.
So I tried:
pi@TimePi:/var/log/mosquitto $ sudo echo "********** 2019 01 06 09:33" >> mosquitto.log
-bash: mosquitto.log: Permission denied
Not a big deal, but why doesn't that work?
Just so I have a "from here" point in the file.