Illuminating the HP49G LCD display?

[n3mmr]

I tested my 49G the other day, and it had developed keyboarditis, i e to start it up you have to push hard on the bezel above the softkeys in order for it to wake up.

So: I'll have to open it up and fix the kbd connector.

So I thought I might try to add some LEDs arranged near the display to improve readability of the rather dim LCD.

Has anybody else tried this?
What LEDs could you use? Where should you connect the LED to minimize the strain on the electronics and so it would only light up when the calculator is on?