This is why I often tell people to use a test light instead of a digital voltmeter. If you stop reading right here and retest what you did already, but with an inexpensive standard test light, you'll find different results.
You inadvertently stepped over the best clue in that you found different voltages at the battery's positive post and the generator's output stud. Those two are tied together by a fat wire, so there has to be the same voltage at both ends. You'll notice the starter solenoid is in that circuit too. Don't pay any attention to that. It is only there because GM often uses that as a convenient tie point so they don't have to run two separate wires back to the battery. That solenoid is not part of the charging system.
At some point the end of the wire at the generator became grounded, either by accidentally shorting it to ground with a wrench, or because two or more of the generator's six internal diodes were shorted. That burned open the fuse link, shown by my blue arrow in this diagram. That is why you see a higher voltage at the generator than at the battery. The generator can be thought of as a pump for electrical pressure, (voltage) and the battery is the storage tank, like the water tower for your city's water supply system. As long as the voltage is higher at the pump, current will try to flow into the battery, but it can't get there because of the blown fuse link. GM's voltage regulators are inside the generator, so the entire system is working properly and regulating at an acceptable 14.8 volts. It's not supplying the electrical system though. That's why the battery is running down as you drive.
The fuse link wire is usually located near the starter solenoid. You'll see at least one piece of heat-shrink tubing on it about four to six inches from the terminal. Tug on that wire to test the fuse link. If it's still good, it will act like a piece of wire. If it's burned open, it will act like a rubber band.
You can buy new fuse link wire from any auto parts store. They may even have special ones for GM vehicles that have the terminal already crimped on one end. You'll need to splice the other end to the red / black wire, then seal it with heat-shrink tubing with hot-melt glue inside. That will seal out moisture. These are typically about 12" long. You can cut them into two or three pieces to make multiple repairs. The length you install is not important. It simply needs to be a smaller diameter than the other wires it protects. That makes it the weak-link-in-the-chain, just like any other fuse, except it is a slow-acting fuse.
Fuse link wires are selected by color which denotes their current rating. Don't try to use a regular piece of wire. Fuse links have insulation that will not melt or burn.
There's one confusing thing related to fuse link wires. That is they form a coating of carbon on the inside of the insulation where arcing occurred as it burned open. The generator's output current can't get through that carbon, but when no current is trying to flow through it, no voltage is dropped across it either. For all practical purposes, a digital voltmeter doesn't rely on current flow through it to take a voltage reading, just like a pressure gauge on a compressed air line doesn't require air to flow through the gauge to take its readings. You start with 12.6 volts at the battery, drop 0 volts across the fuse link, carbon, and rest of the wire, so you end up with 12.6 volts at the generator, as you found.
Now try to do that with a regular test light with an incandescent bulb inside, not one of the new fancy ones with all kinds of electronics. The bulb requires current flow through it to light up, and that current can't get through the carbon track. It will correctly show 0 volts at the generator. Another way to see this is to take the reading with your voltmeter, then while you're seeing the 12.6 volts, touch the test light there at the same time. When you do, the voltage will drop to near 0 volts.
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Monday, February 22nd, 2021 AT 8:37 PM