The battery light may illuminate on the instrument panel because the alternator wire harness connector is damaged. A new connector kit is available and should be installed to correct this concern.
Car Problem Reports
Ford F-250 Battery Light Due to Damaged Alternator Wire Harness Connector
Ford F-250 Problem
Average Mileage: 122,871 mi (15,614 mi - 211,000 mi)
Visitor, 1996 Ford F-250, 211,000 mi
conductors inside alternator connector had become loose; bent them tighter and applied dielectric grease to correct.
Battery light was on and gauge indicated not charging at all. Cleaned the harness connectors and bent them closer.
Problem solved. Tip came from reading other's problem and solution posted.