A design I worked on a few years back (a telephone dial with opaque buttons) used a transparent, one-piece moulding through which the buttons poked. A limited amount of this "web" moulding was visible around the keys; with careful design to enhance TIR (Total Internal Reflection), a single low-power green LED fed from the phone line (impressive in those days) illuminated a rectangular matrix of some 12 keys plus 4 others a short distance away. The keys remained opaque, but could easily be located in the dark by the peripheral lighting from the TIR web. This is also seen on many other commercial products these days, including Pioneer and Philips car radios.
What about that as a possibility, then? I think I suggested this a few months back in Wish List somewhere if you want to check the thread.
Alternatively, it strikes me that since you are using a perspex front panel, you could use the internal light-carrying capability of the optical cavity within the sheet to illuminate the buttons from the side without affecting the amount of transmitted light through the front panel (going perpendicular to the enclosed TIR path).
I mean, you guys are literally a few hundred metres from the Pilkington glass research centre in Cambridge, and C Uni is a world research centre for optics and light propogation in restricted cavities (optical fibres) - can't you cadge a bit of advice locally?
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One of the few remaining Mk1 owners...
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