I'd probably need to get something custom made, unless you know of another way to do it?
Well, it's something most people that have done electronics have built a couple times. It should be that difficult to create a tiny version now... It depends how many millimeters you can spare inside.
It would probably require a microcontroller programmer, though, unless you go for a kit that already include a pre-programmed microcontroller. Using a kit like this:
and soldering the LEDs directly on the chip would probably do it (the left button isn't required, and the top resistor have far smaller alternatives).
Video:
https://www.youtube.com/watch?v=GbhU1BBO0TQ
(in fact, you may already have enough space to put the kit without modifications inside... you would just have to bend the leds sideways)
The chip above is small enough to enter in a 1x1 brick space, but if it's still too large, there's a version that's a good chunk smaller than a 1x1 tile. It would be harder to solder, obviously
I have no doubt you can fit half a dozen small CMS diods in a 4x1 tile volume. Since you can put the battery anywhere, it's just a matter of running the wires.
I may really try it, although probably not before summer... I want more free time :/
Edit: to give an idea of scale, quick and dirty:
That's the LARGE version of the chip (the one seen above). Yes, there's a version far, far smaller.