Hi, based off the very first post you made your alternator has altered its last nator. If you have a good local rebuilder take it to them, if you dont, opt for a Denso reman unit from a reputable retailer. Note: you may need some of the hardware or boots plugs etc. from your current alternator to fit the reman unit. Do not send in a core until you have fitted and tested the new unit. Hope this helps

 

To elaborate, the reason to test battery after rest, is batteries can hold what is called a surface charge.

A battery that needs to be replaced, no longer reliably start car, can often be charged, and test fine for voltage.

But put any real load on it, or even just let it sit, and that charge quickly bleeds away.

Think of it like this. Two 9v smoke alarm batteries in series is 18v. But that ain't startin any engines. Voltage is there, but not enough capacity. Just like a dying car battery.

Its very clear your alternator output voltage isn't where it's supposed to be. But that could still be the battery, holding the voltage down.

Its probably not the battery, just mentioning that just in case.

As already mentioned, check connections. That includes battery cables. Where they clamp to battery, as well as cable condition. Check them all the way to opposite end. Look for frayed, etc.