More than likely, if everything is original, you need to adjust the voltage regulator. The older classics had adjustable regulators with contact points that get dirty and an air gap adjustment.
You may have buildup on the contacts, you may have buildup on the generator brushes.
The light will also glow with an overcharge problem. Or with a problem with the dash resistor wiring.
Best you can do is check it with a DVOM to find out what it is actually doing. From the battery, generator, regulator, "idiot" light, resistor, etc.
Own a 61 Galaxie 500 4dr Wagon with a 292. All original and even vacuum wipers that I inherited from my GrandDad. It's been a challenge at times, but a lot of fun. Been working on the classic Fords for over 30 years.