I just went over real quick. Have you tested voltage drop over the starter seloniod. That click noise is coming from relays in the dash fuse box location. I had a few ford trucks do the same thing( and before any one says anything its a ford they use the same setup). The battery cable is going bad. One day its good the other day its bad. When its bad it will show low voltage at the starter selonoid but have normal voltage at the battery. When you go to start it will click then everything will act like they are seeing low voltage.