[Steeveedee]

That cylinder below the regulator is a "condenser"- a capacitor, used to reduce radio noise from the voltage regulator switching. I'd suspect that you have a failed diode in the alternator, or that the voltage regulator is bad. One of our guys has much more knowledge than I do about troubleshooting electrical; he'll likely be around soon with more on how to check that out properly.

How did you test the alternator to verify that it is good? I hope you didn't just pull a cable off the battery to see if the truck continued to run.