Further refinements to the personal backup idea.
.
I've incorporated all of Werner's excellent suggestions, and since
I found I never referred to the tar listing, that's been omitted.

In examining the remaining contributors to the 'personal backup', I found
that not only is .mozilla the real space hog, but its caches are its
biggest contributors. It is possible to clear at least one of these caches
with a quick trip to the IceWeasel Edit>Preferences GUI before making
a backup, resulting in a great reduction in the size of the stored file.

A revised listing is as follows:
Code:
#!/bin/bash
#
# new.backup2: do 'chmod +x new.backup2' & 'chown root:root new.backup2'
# Before backup, Go to Edit>Prefs on IceWeasel & 'Clear Now' the Off-Line cache.
#
cd /; STOR=/mnt-system/update$(date +'%m%d%H').tar.gz
echo -e 'Compressing data; patience, this may take a little time..\c'
tar -czf $STOR KNOPPIX-DATA/home/  KNOPPIX-DATA/etc/ \
               KNOPPIX-DATA/root/  mnt-system/boot/syslinux/syslinux.cfg 
echo '.Done.'; echo 'Restore using the command, tar -xzf '$STOR' -C /'
#
exit 0
Now if some clever person here will inform me of some appropriate API,
assuming there is one, we might automate that effort as well. This is
to say that I haven't been able to 'exclude' from the tar inclusion
the Cache & OfflineCache directories from ~/.mozilla/firefox/*.default/
which are the culprits I'd like to exclude.