Battery not charging?

I can't stress this hard enough, never remove a battery cable with the engine running. That is a very easy way to destroy every computer on the truck. It's a "test" mechanics did in the 1960s when they didn't understand how these simple systems work. To further complicate the issue, depending on how the voltage regulator is designed, an engine can stall with a properly working charging system, and it is possible for an engine to keep running with a defect in the charging system, so that "test" is not valid.

The place to start is by measuring the battery's voltage with the engine off. If it's good and fully charged, it will be close to 12.6 volts. 12.2 volts indicates it's good but fully discharged. Next, measure again with the engine running. Now it should be between 13.75 to 14.75 volts. If it is, that only means it is okay to do the rest of the tests, but those require a professional load tester. Specifically, we want to see "full-load output current", and "ripple" voltage.

Full-load output current will be very close to the design rating of your alternator, 0.0 amps, or exactly one third of the design rating. One third of that rating points to one failed internal diode of the six. In that condition, you can get enough current to keep the engine running, but as additional loads are turned on, the battery will have to make up the shortfall until it slowly runs down.

If you let me know what you find up to this point, we'll figure out where to go next.