Someone also asked me about this regarding their SR16.
It wasn't a guy called Bert from germany was it?
I've been working on this on and off on the SR16 for a while. You can't light these screens from behind unless you peel of the silver backing foil and i've found it impossibly difficult to light them from the side even using the smallest ultra-bright surface mount LED's.
I suppose you could peel off the silver foil and stick some kind of diffusion sheet behind the screen but getting any LED's far enough away from the screen to actually get any light diffusion would be tricky.
The best way i came up with doing it is to either use two small cathode tubes mounted above and below the screen like we do on our TR707 mods, or even better to peel off the silver backing foil and stick a bit of EL sheet behind it. The major problem with either of these methods is power. The backlight inverter for either cathode tubes or a bit of EL sheet needs 12V DC and a whole lot of milliamps. Annoyingly the SR16 runs on 9V AC so short of adding another power socket for the backlight or completely rebuilding the power supply i'm not entirely sure how to go about doing this. Another problem is that the interiior of the SR16 has no RF shielding and is very prone to picking up noise, so it'd probably pick up no end of crap from the invertor.
Presumably the regulators in the SR16 could cope with feeding it 12V AC and it wouldn't be that hard to take a separate feed from the power socket and rectify it for use as DC power for the backlight invertor. I'm just wondering if anyone has any better idea of how to go about this.