How do I do a Windows system image?

Windows System Image is the most poor option you can choose.
There are many PROFESSIONAL grade backup programs that do it much better FOR FREE (they did it before Windows put this poor imitation in their OS).
They have more cool options, are more transparent, and very easy to use and understand:

https://www.paragon-software.com/free/br-free/ 
https://www.ubackup.com/download.html 

If you keep insisting though, check the drive properties, see if the Used Space/Free Space are really not lining up.
If they do line up, it's because Windows Backup uses it's own folder structure, and sometimes even change a full drive to its own use (so no other program can use it anymore).

Both times the image does not show up on the external drive

what's shown in the designated drive after the Windows reports the backup or Windows image has been done?

aomei :  https://www.aomeitech.com/aomei-backupper.html
a list :  https://www.techradar.com/best/best-disk-cloning-software
just be sure to take the whole disk...

maybe he did not choose the storage location on external drive - and stored it in C:
search for a file with the name you gave the restore

Thanks to the experts.  Much appreciated.
capreol