Airport Express Extending a Network via Ethernet not working via wall socket

Just to be sure, based on your diagram, is the IP address provided by the Extreme consistent, at both the Extreme's LAN port (yellow), and the wall port (blue)? Is the Ethernet wiring, within the wall, wired as "straight-thru?"

You know that the Express is set up correctly, so the issue is either with the wiring or one of the Ethernet wall plugs. To verify, connect the Express directly to the AirPort Extreme using another Ethernet cable......as long as you like...... to confirm that it works correctly that way.

The house Ethernet system.......if it is wired correctly......will act exactly the same as a separate Ethernet cable.

If a plug is not wired correctly or if there is a break in one of the 8 Ethernet wires, you might be able to get a computer to work with the Ethernet wiring........because it does not require that all 8 connection points are wired correctly.

But........you won't get away with an Ethernet wiring problem when you add another router, which requires that all 8 connection points are wired correctly at each port or plug.

Bottom line......the Express will work correctly when the house Ethernet wiring is working correctly. Unfortunately, it is possible that there are more errors in your home Ethernet wiring system. Check by connecting the Express to other Ethernet ports in other rooms.

If you set up the AirPort Express to "extend using Ethernet" when it is connected directly to the AirPort Extreme, then it will not change settings if you move the device and connect it using Ethernet.......assuming the Ethernet wiring and plugs are configured correctly.

So, the first thing to check would be to move the Express back so that it is connecting to the AirPort Extreme using the wired Ethernet connection and check to see if the Express has been set up correctly using Ethernet.

Open AirPort Utility

Select the AirPort Express

Click Edit in the smaller window that appears

Click the Wireless tab at the top of the next window

If the Express has been set up correctly, the setting for Network Mode will be "Create a wireless network"

Is that the setting that you see when you run this check?

If you see that the setting for Network Mode is "Extend a wireless network", the Express has not been set up correctly. That setting is used only if the Express will connect wirelessly, not using Ethernet.

Please report on your findings.