Car only clicks when the ignition is turned. I think it is the starter, since the battery seems to be okay.
The starter solenoids on the expeditions are known to just quit with no warning. Before replacing the solenoid however, the battery should be fully charged and load-tested to eliminate it from being the issue. The solenoid is tested via a voltage check at the control wire off the solenoid. You may want to enlist the help of a mechanic, like one from YourMechanic, to test the starting system components and make the necessary repairs.
Our certified mechanics come to you ・Backed by 12-month, 12,000-mile guarantee・Fair and transparent pricing