Ford used 2 different wiring setups on the 1g alternators with external regulators, depending on wether it had a warning light or an ammeter. The way you have it is correct for an ammeter setup. For a warning light setup, a goes to the starter solenoid battery hot, I comes from the ignition switch through the warning light (don't use a LED for this and put a resistor parallel to the bulb so it'll charge if the bulb blows), f goes to field or fld on the alternator and s goes to stator or sta on the alternator.

Most aftermarket regulators can be swapped interchangeably, but Ford did use a separate part number depending on how it was wired originally, I'm not sure if your regulator is universal or not, that's something to check.

Even if you don't run a light, the way you have it should work provided the regulator can work that way.

Either way it should not be getting warm with the key off, that shows a current draw through it which will kill the battery.