When you go to apply the thinset, you'll be using a trowel with a notch depth appropriate for your tile size. It will, most likely, be somewhere between 1/4" and 1/2" (though a 1/2" notch is mostly for big tiles, most commonly used on floors, so not likely to be used on your RV wall).
Get an aluminum or plastic* U-channel of the proper depth to match your notch depth and just wide enough to put the LED strips in. Apply the channel to your walls where you want the LEDs to run (glue, screws, whatever makes you happy), install the LED strips, then apply your mortar up to the edge of the channel, but not within the channel.
Unless you're using very tiny tiles, they should more than span the width of the channel, meaning the tiles will have adhesive on either side of them so they'll be held in place. With the motion of a vehicle moving down the road and bouncing across dirt roads in an RV park, there's a chance of the tiles falling off due to sub-optimal adhesion. You might consider changing the pattern/tile choice to something that will work better spanning the non-glued space of the channel.
*Use a material/color that will blend the best with your tile choice to minimize visibility of the channel itself. Aluminum might be most visible through translucent tiles because the AL channel will be thicker, while plastic would probably be least visible because it could be very thin walled (there's no structural need for a thick piece of plastic here).