What can I use to create a "chair rail effect" for my outdoor privacy fence to separate the two different materials?
Fabric.
You already have that beige fabric up.  It is already attached to the wood.  Go back to wherever you got the beige fabric and get some in gray.  Fold the edges under to make a strip the width of the wood underneath.  Attach the strip to the wood with staples or upholstery nails or whatever you used for the beige fabric.  Of course there will be a layer of beige fabric underneath.  That is fine.
You will have a line in a different color at the junction of wall and beige fabric.  It is lightweight and easy to attach using a method you have already successfully used for the beige fabric.  It can a different color as you request and a textural echo of the beige fabric above.
Plus if you don't like it, it will be easy take it down.  You could do a mockup first using paper as a test run.