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Basically when the chip sees 12V (from the flashers or the brake pedal), it delays the activation of the outer two lights. The inner light comes on instantaneously and isn't controlled by the chip. After a certain amount of time, the chip activates a circuit that allows the 12V to turn the center light on, and then the outer one.
I was going to do a write-up, but I used programming software to write the code and a device programmer to put it on the chip. Unless you have access to these (I use them at work), they would far outweigh the cost of just buying the sequential taillights set from somewhere else.