Charging issue

12.4 Volts at the battery with nothing on is a bit low. Put it on slow charge and see if it will come up.
9.4 at the alternator shows a voltage drop. What was on when the measurement was taken? What did the ammeter show?
This is what you need to know to evaluate a voltage drop.
Voltage only drops when electrons move, or try to move though resistance.
It'll come up, it's low from me fighting with this issue most of yesterday (it's on a slow charge right now so I can put it back in my other car). Key was on but radio and lights are off, it's the same with it running or just key on. Ammeter stays to the left side, I'm going to guess there is corrosion someplace.