Follow-up. Apple was able to help me re-format the SanDisk, which after doing so, the SanDisk did appear on my desktop. We then chose the SanDisk to use for Time Machine auto backups, and this time, Apple had me TURN OFF the "encryption" choice at the time of setting the external up to use for Time Machine.
The external drive has been working for 24 hours, and Apple will follow-up with me tomorrow and then again at a later date.
SanDisk technical support had also suggested it was an encryption error that Apple would need to be notified. All good today! It was ironic that my previous external failed, and the new one failed in the same week but so far so good.