Low charge when hot.

Mattax said

It would seem its not stock.
In daytime, without the lights or anything else on, battery voltage should have not dropped down to 12.0 V.
The fact it came up to 12.5 V with a small change in rpm suggests the alternator is partially working.

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The only thing not stock is it has a relay that accounts for the crappy bulkhead connector and a bypass wire from alternator to the starter relay to help charging. Everything works great when it's nice and cool, only when it's hot does it barely charge.