I am dead center in the, "check the wiring," camp. Be sure to look at the gound cable from the battery. The ground cables I use has an interin ground lug that is attached to the inner fender, under one of the retaining screws for the voltage regulator. The other is attached to the passenger side cylinder head under a bolt. If either the interim ground cable lug, or end lug, is missing or not tight, it can cause all kinds of havoc. Also, on the rear of the alternator, the wiring harness is supposed to be attached to the alternator using a ground stud and a nut.
https://www.youtube.com/watch?v=GmDi0y2COzc
In the event the wiring harness to the alternator has been damaged, or the insulation for the wires has been pierced a large number of times, you can get the charging system sub-harness from a variety of sources. Just Google on the following text:
"
1973 mustang charing system wiring harness"
I have seen more times than I am comfortable with situations where someone has replaced a battery, alternator,
and voltage regulator ("because when one goes bad it affects the others" or some such implausible excuse), and the problem turns out to be the wiring and/or bad ground, where there is an intermittent open circuit due to something as unusual as the wire's conductive material inside the insulation has fatigued and broken, or in one case the brush holder in a Ford side terminal alternator failed to hold the Field spade terminal in place, which kept the Field current from ever getting to the alternator's rotor windings. I saw evidence on that car (the aforementioned Field circuit issue) of someone having poked and prodded the alternator wiring so much that I had to replace that sub-harness before I could move onto diagnosing what was a clear problem where the battery would only hold a charge for as long as it could while its charge was being depleted by the ignition system and other electrical loads. The prior owner had replaced the battery, and the reculator. It turns out he had replaced the alternator also, and the replacement rebuilt alternator is where I found the problem. If you are curious I did a video on that situation:
https://www.youtube.com/watch?v=-ur-4TSZoRU
In the photos below it looked to me like the spade terminal for the Field circuit had broken off. But, actually its retaining tab for the Field spade terminal in the brush housing did not engage or was worn/broken. So the Field spade terminal had actually been pushed back into the brush housing, where it was not able to make (constant) contact with its female spade terminal in the harness plug. I placed the term "constant" in the preceding sentence because there were times when the voltmeter in the car's Dakota VHX analog instrument panel when the gauge did show 13+ volts, but that was fairly rare, and would only last for a few occasional moments. That, of course, added to the baffling situation, and may well be why the prior owner had decided to take a shotgun approach when replacing the regulator and battery, whether they were actually in need of replacement or not. Had I not seen the cause of the intermittent charging I would like to think I would have not succumbed to that kind of approach (it.s not may nature anyway, FWIW). As it was I had already replaced the charging system sub-harness - but mostly because of how much the wiring insulation had been perforated with test light probes - not because I though it was causing the no charge itself - but I was hoping that perhaps there was a fractured wire inside the insulation on one of the wires. No such luck.
