I agree, the speaker wires headed into the crossover are not in the rats nest behind the headunit, so they likely
terminate in the trunk, though they may be hidden under the dashboard somewhere.
Behind the speaker you can see the factory speaker wires (gray/red and green/yellow). While I would recommend
ultimately installing an amp, you should be able to connect them to the crossover and get things working for now.
If the previous owner didn't monkey with them, the wires should have a connector on them. Get some so you don't cut any wires, plug them into the factory speaker wires, and run lengths of wire from them to the crossover
inputs (in place of the ones there now). You should insulate the ends/terminals of any wires now left unconnected with
electrical tape so they don't bounce around and short something out.
Later you can go back to those the fancy wires if you add an amp.