The way they always used to do that kind of thing at Blackpool Illuminations was an array of motor driven rotary switches.
Using DC, and mixing the rotary switches with diodes to combine outputs from the switch selectively, there are a heck of a lot of combinations and permutations available when offering power to sticks of LEDs.
Most rotary switches came with a combination based on 12 - 1 pole, 12 ways; 2 poles 6 ways; 3 poles, 4 ways; 4 poles 3 ways etc. It is possible to get kits to stack wafers, as well. Just needs more muscle to move them. Arranging one to work with a linear slider could be a tricky proposition, gearing a motor to the switch would be easier. Double reduction worm springs to mind, much like a motor driven tuning condenser that I got when but a lad from one of those wonderful govt surplus shops that were around back then.