David and Dave,
I meant to post yesterday but am busy with a two day festival with our model boats for AvaGo so time was short. Still, if you are still searching then DM is correct, a programmable chip board for example Arduino, Adfruit, Pollulu etc will certainly do the job.
My experience is with the Arduino (I used one to activate and operate 13 navigation buoys with their correct flashing light sequences so that one, two and even all can be on together) and this can certainly be programmed to do as you want.
It is very simple to write the instruction on a PC. Most people think computers, code, RUN.
All your system would require is three random choices made by the code, how many lights, on what circuit for how long. The power supply required is 5.5V and the maximum power out for LED etc is 100mA.
Send me a PM if interested.
I also built a timer system for control units of boats, that was based on the 555 chips. Their use would be a bit more complicated as you would require to build a circuit as well, so a programmable chip would be better.
KIm