Quoted from LTG:
Another way, you could unsolder the wires from the small circuit board in the top of the bookcase and pull them through to the bottom and the fish them back up and resolder.
Just get each wire back in the same spots.
LTG : )
I just did this about a week ago to replace my bookcase base. It wasn't obvious to me how to feed it through without unsoldering the wires from the small circuit board. While it's not hard to disassemble it, it is time consuming.