Catalina install fails when installing on external USB-C hard drive (SSD)

First, verify that the external disk is not encrypted. If it is, then reformat it and do not opt to encrypt the disk. Second, verify you formatted the SSD using APFS format. Third, re-download the Catalina full installer: Get macOS Catalina via Software Update.

When you run the installer be sure to change the target disk from the default disk, the internal disk, to the external one. Some installation problems may be solved by installing from Safe Mode:

Boot Into Safe Mode

1. If your Mac isn’t already shut down, then shut it down and wait at least 30 seconds before rebooting.
2. Immediately, at or before the chime, press and hold down the SHIFT key. 
3. Release the key after the Apple logo and progress bar appear.
4. Safe mode startup is much slower than normal startup, so be patient.
5. When the Login Screen appears enter your admin password. If you use automatic login, then this means you are in safe mode.

The only thing that I have not tried from your suggested list is to boot to safe mode and attempt it. I did download the installer a couple of times and I have now made a USB install drive from it so I am pretty sure that was not the issue. I will try Safe Mode. Thanks for your response.