No anonymous user role in CiviCRM » Administer CiviCRM » Access Control WordPress Access Control
It seems that there were two moving parts here. The first was properly setting up the base page the second, and more complex part, was properly creating and naming the Anonymous User role. With the former properly in place, the latter seems to be the fix.

From what I can gather, it seems that on install Civi 5.10.4 did not create an anonymous user role. It was not listed in the Wordpress Access Control. The role needed to be created manually and it needed to be properly named. I used the User Role Editor plugin which gave good control. I now realize that I was not properly naming the new at first, calling it simply "anonymous" which did not work as hoped. Looking at the civi code provided clues to correctly naming "Anonymous User" as "anonymous_user". Creating that role and assigning the permissions seems to have resolved the issue.

See here
https://lab.civicrm.org/dev/wordpress/blob/master/includes/civicrm.users.php#L253

The correct permissions are here:
https://lab.civicrm.org/dev/wordpress/blob/master/includes/civicrm.users.php#L272

Thanks to the two people who provided clues. Sorry if I didn't properly follow custom here, I'm very new and getting the hang of things. I'll try to watch and learn.