I also have this issue. I was wondering if anyone could help me. Pressing the button accomplishes nothing. I'm going to restart, allow the system to update and then see what happens. I love my Surface RT! But lately it's been so slow, I can't stand using the internet and have defaulted to my Lumia 830 for any common web browsing. But for it's main purpose (writing and editing documents), it still functions very well.
I loved the backlighting on the type cover 2

What happened? How can I get it back? The rest of the keyboard is fine, by the way.
Got it!
So I did some research on this forum (which admittedly I should have done in the first place), and I found out what the problem was!
My keys were technically working. They just weren't lighting up. THe F1 and F2 buttons were functioning as...F1 and F2 buttons instead of enabling the backlighting.
So here's what I found, in a post from 2014 that fixed my issue:
An intermediary fix for this problem is to hold the Fn key while pressing Home, End, PgUp, PgDn and the others at the first row.
Ain't nobody got time for that!
This happened out of the blue because I had accidentally pressed Fn + Caps on the keyboard.
Pressing these 2 keys again reverted back to standard behavior.[[B[/B][/B]
So I just kind of held down the caps lock and the 'Fn' button at the bottom right of the space bar for a few seconds and then I turned on the backlighting! So excited to have this back! I hope this helps you, too!