Shane, can you take a picture where your solenoid is? It sounds like it’s been moved from the factory location. Also, be sure to check your ground wires.
Now that is strange, never seen a setup like that on any of my Lincolns. Does your starter positive lead go to one side of that? Maybe get me a couple wide shots of the battery & inner fender area?
Yes, the the positive starter cable goes to that box. It’s an odd setup, but the car is unmolested and stock as can be from everything that I’ve learned so far.