With the engine running you should measure the voltage being maintained by the regulator anywhere that is supposed to be "hot". With the engine off (key in off position) you should measure the charge the battery is holding across the battery terminals.
The old electro-mechanical regulators were "supposed" to be set at 13.65 volts if my memory is working. The solid state replacements run closer to 14. And most modern alternators with built-in regulators run even a little higher. I highly recommend replacing any electro-mechanical regulator with a solid state replacement. The charging system operates much better.
If the voltage looks OK at idle, but increases as engine speed increases, that's a regulator problem. If the voltage looks OK, then jumps high, then drops back to normal again suspect a sticky electro-mechanical regulator.
Batteries are usually 2.1 volts per cell (12.6 volts). However decades ago (80s & 90s) I ran Delco batteries which were closer to 2.2 volts per cell (13.2 volts). A Delco battery that measured 12.6 was undercharged. My point being that 12.6 volts isn't necessarily the sign of a healthy battery in each and every case, it depends on the battery.
Alternator diodes fail sometimes. On some occasions an alternator with a bad diode makes a growling sound that sounds like a bad bearing ... but its not its a diode. If a diode fails open the alternator will have a reduced output. If the diode fails "shorted" the alternator will have AC current in the output. Anything that has computer circuits (engine management, stereo) may display problems if the charging system has an AC component.