Is there a way to enable Basic Auth for only one specific type of node? Can't really find much useful in the way of googling.

I have a special content case on my site where I have created a page template which displays a series of blocks in my theme code. To apply this template to this particular page, I made a custom node type for it. However, this content is (and should be) restricted only to users with a certain permission, which I accomplished via the Content Access plugin.

I want to use wkhtmltopdf to output a PDF of that page for internal use. The only way I think I can get the node instance to allow wkhtmltopdf to view it is to run wkhtmltopdf with the --custom-header flag with an Authorization header. I need this to happen once per day, and was thinking of setting up a cron task to run wkhtmltopdf nightly on a Linux system (so far I have just been testing it manually on a Windows system where the node had no permission requirements and everything seems fine).

I know that enabling basic auth for certain paths is a thing I can do using a plugin, but this content is not defined by a plugin and is just a node I created using the Drupal interface.

Is this possible, or do I have to tear it down and start over and build a new custom plugin?
Probably there is no one here, that has tried the method you've described. I would start with a custom entity, use the basic auth or create a new authentication provider and apply this for the entity route. You can do this with drupal console within a minute.

And you don't need contrib code to configure access for the custom entity, because here you can do what you want in core. I wouldn't use an Access plugin from contrib, until there is a stable release.