Hey Rob,

I had this exact problem about a year ago, LED on the switch will turn on but the rear window stays icy cold. My problem was just a burned out fuse (it actually melted and fused with the plastic wire holder), and it is located under the rear seat on the passenger side (RHD).

I didn't test any relays after I replaced the fuse, I just saw a burned out fuse and replaced it and all is good ever since. Good thing too, if the fuse blew out again shortly after then I know I have an auto-electrical problem, which isn't fun to diagnose and repair.