There is a common problem with high mileage altenators. One of the alternator diodes goes bad and the light comes on. The alternator will still produce enough power, as long as you are not running the AC all day long on a trip, with other electrical loads like headlights etc. When the second diode burns, the battery will gradually run down and die. All alternators have 3 diodes. Take it off and take it to a parts store to get it load tested and you will have your answer. You can test it your self if you have a DMM or VOM and know how to use it. Just connect the meter red + lead to the + terminal of the battery, and the black or - lead to the - terminal of the battery. It should read around
12 volts with the engine off. Then start the engine, read the meter, it should say 13.8 or a little higher, maybe 14, or 14.4. Then start adding load to the system by turning on the AC with the blower on high, the headlights wipers etc. Keep reading the meter. If the voltage drops below 13.8 at idle, and going to fast idle doesn't cure the problem immediately by reading 13.8 or better, you most likely need an alternator. But, after all it is a Ford, so there are no guarantees. Most alternators last about 70 to 100k miles, less in dusty conditions. They have a set of carbon brushes that also wear out, especially in dusty conditions, and the more load you put on the alternator, the quicker they wear out as well. Good Luck.