Yes, the '60 Falcon had a generator, rather than an alternator.
To the best of my recollection, the first alternators on US-made cars were on Chrysler products, in 1962 or 1963.
I think you’re right, Ford switched in '65 or so.
You guys are great! I feel like I got every spanking bit of information available in the universe. I will 1) get the battery load tested and replace if needed. Good or bad, I will 1) Clean off the corrosion and apply something to keep the terminals clean. 2)
tighten the cables.
If it happens again, it’s back to the neutral safety switch theory – and vice versa on the steak dinner. (We both win. 
Ann
Idling an engine with A/C and radio on would probably slowly drain a battery. However, the A/C will not work with the engine off. If the engine was shut off and the key turned back on, the A/C clutch would be engaged along with the fan and radio, the battery would go pretty fast. My guess is that the battery is OK after charging. It would be a good idea to clean the cables tho.
“To the best of my recollection, the first alternators on US-made cars were on Chrysler products, in 1962 or 1963”.
VDCdriver: You are close. I believe Chrysler introduced the alternator in its 1960 models. Even the Valian had the alternator. The other manufactureres slugged it out afor a couple more years with the generators.
Transistor radios became popular in cars about 1963. I remember my parents’ 1960 Rambler had a vacuum tube radio. However, the tubes were designed so that the plate voltage was 12 volts. Earlier vacuum tube radios had a plate voltage of 90 volts or more, so a vibrator or pulsator was needed so that an auto tranformer could be used to step up the 6 or 12 volt d.c. voltage. After the voltage was stepped up in this way, a rectifier had to be used to convert the power back to d.c. By 1963, the transistor had taken over. My parent 1963 Studebaker Lark and 1963 Buick LeSabre each had transistorized radios.