Adam Aglionby wrote:
Simple answer would appear to be to modify a desk lamp with LEDs and
take 12V power from the computer PSU.Disadvantage of light shutting
down with computer.
Or hack the UPS to obtain low voltage D.C. source from internal
batteries.

Adam

Even easier would be to get a keyboard that is rear illuminated, but
those are sometimes pretty cheaply made or horribly expensive.

Also, you could get a USB powered LED light, or make your own (Clive's
site has some ideas