A ford regulator or Ford aux relay? Sounds like it's either the aux relay, or you have a bad cable/cable connection (Could even be the crimped connection on your battery cables.)
If the battery checks out ok, and the Alt checks out ok, all it can be is wiring (Or the aux solenoid if yer using one). ORRRR the engine is toast and much harder to turn over, but I dun think that's it! lol.
Ray