Did not work
You might want to consider using Apple's setup "wizard" to apply the correct settings to the Express.....virtually automatically. So, you don't need to worry about exactly what setting to choose or deal with other jargon like Bridge Mode, etc.
If you decide to try this, please follow these instructions carefully.
Select the AirPort Express that you want to connect to the Time Capsule and temporarily move it close to the TC.
Use a short spare Ethernet cable.......any length will do.....and connect from one of the LAN <--> ports on the TC to the WAN "O" port on the AirPort Express
Power up the AirPort Express for a minute or two
Hold in the reset button on the back or side of the Express for 7-8 seconds and release
Allow a full minute for the AirPort Express to restart to a slow, blinking amber light status
Click the WiFi menu at the top of your Mac's screen and look for a listing of New AirPort Base Station. Just below that listing, click directly on AirPort Express
When you click on AirPort Express, that will get the AirPort Utility setup "wizard" up and running. It will take a few seconds to display a screen that looks like the example below, except that you will see your devices pictured and the name of your network displayed.
Type in a device name for the AirPort Express in the space next to Base Station Name
Click Next
Watch the next screen very carefully to see that the AirPort Express is being set up to extend using Ethernet. This will confirm that the setup "wizard" has picked up the Ethernet connection between the TC and the Express, and the correct settings will be applied to the Express.....automatically.
When you see the message of Setup Complete, click Done.....and the AirPort Express is now set up with the correct configuration.
Power off the Express and move it to the desired location
Connect the Ethernet cable connection to the WAN "O" port on the Express
Power up the Express
If the Ethernet cabling and Ethernet switch are working correctly, then so too will your AirPort Express be working correctly as well at its new location.
You can set up other AirPorts the same way if needed, just remember to assign a different device name to each Express to keep things organized.
Please post back on your results. If you are curious and want to take a look at the settings that the "wizard" has applied, you can use AirPort Utility for that purpose. You might be surprised to see what settings were actually applied to the Express.