Good morning! I am building two built-in bookshelves, one on either side of a window. I have preexisting sconces centered on the walls where I'll be building the shelves. I'd like to use this sconce wiring to install a library light on the front of each bookcase like so (I'm thinking each bookcase will actually be made of two narrower bookcases with a gap between them to run the wire through-creating a center divide with the library light mounted on each).

How would you do this? Can I just use wire caps and same gauge wire to extend the wires from the junction boxes, run that wire through the gap between the bookcases, then connect to the sconces? Would the wire need to be secure or enclosed in anything? Is there anything I'm missing?

I am a complete novice and don't want to do something dumb but this seems simple.