@CDNPilotDave 

Hi,

When the printer is connected behind the RE505X you will most likely need to connect to it by using the printers IP address.

After Windows failed to "find" a printer it should show you an option that reads something like "The desired printer is not listed -> Add a device manually".

The "Add manually" dialog should give you an option to add a printer by supplying its IP address.

In case you don't know the IP address of the printer, then look it up in the clients list of your router.

  @CDNPilotDave When referincing the router's client list the RE505X is shown twice, once for the 2.4GHz band and once for the 5.0 GHz band but unlike all other attached devices there is no IP address assigned for either band. The printer has a an IP address assigned. In trying to narrow this down can I assume that the ethernet port on the left side of the RE505X is a proper port for the printer?

  @CDNPilotDave 

The Ethernet port on the RE505X is a regular Ethernet port. 
However, the techniques used by these "works-with-any-wifi-router" extenders introduce certain inconsistencies. That applies to client devices that are connected to the extender via the Ethernet port as well as via Wi-Fi.

Anyway, are you able to access the printer via its IP address?

Network printers usually have a small web server built in (at least all those that I have ever worked with did). So, if you enter the router's IP address in a web browser on your Windows computer and you see a webpage of the printer showing up, then this would confirm the router is accessible via the RE505X's Ethernet port.

By the way, do you mind posting the make and model of your printer here?