Well that may not be true
Battery cables and posts are fine because we're running the radiator fans directly off the battery and they work fan.
More detail on the fusible link?
If the fan has a direct lead to the battery + and is grounded to the battery - all you know is your battery has juice.
If the ground from the battery to the engine block is bad then nothing else will work.
If the lead from the battery to the solenoid is bad nothing else will work.
The harness pulls power from the battery side of the solenoid. The main power wire had a fuseable link which acts like a circuit breaker in case of a short to prevent a fire.
An electrical fusible link is a type of electrical fuse that is constructed simply with a short piece of wire typically four American wire gauge sizes smaller than the wire that is being protected. For example, an AWG 16 fusible link might be used to protect AWG 12 wiring. Electrical fusible links are common in high-current automotive applications. The wire in an electrical fusible link is encased in high-temperature fire-resistant insulation to reduce hazards when the wire melts.
You may have shorted and the FL may have done it's job. Start at the battery and check all the connections. Pay close attention to the battery side of the solenoid. Make sure not only the battery end of the ground cable is good but also the other end. You can turn your lights on and then use a screwdriver between the - battery post and some bare metal like the alt bracket to see if a ground is the problem.
If all those connections and cables seem good trace the wire from the solenoid to see what it looks like.