TimeShift not backing up to USB flash drive
Since I posted the question, about midnight I discovered the following site: https://ubuntu-mate.org/faq/usb-image/
It didn’t really answer my question, but I followed the section called, Ubuntu/Ubuntu MATE. Even though I put Ubuntu Mate on the flash drive, I was then able to do a full TimeShift backup on that flash drive. I don’t know why that happened (I am basically a newbie, somewhat intermediate user of Linux); but I am happy I got the backup.
Thank all of you for your assistance. Linux does have a wonderful and rapid reply Community.