Thanks
gophert .
It's hard to tell from my poor excuse for a photo, but the translucent panels are actually moss-green in colour. I'm not too concerned about colour-shifting of the LEDs through the green filter (although, admittedly, I hadn't even considered the effect on the flashing red LED until you mentioned it).
The circuit will actually need
two LEDs: a white non-flashing LED which will need to be reasonably bright at all angles, as it will be the main source of internal illumination for the wayfinder, and a red flashing LED which can be more directional (in fact, I might even put a housing on it so that it only shines through one of the translucent panels). For the flashing LED, I believe you can buy LEDs with integrated chips that make them flash, is that right?
If that's the case, could I simply connect a non-flashing white LED and a flashing red LED in series?