Electrical problem?

NEVER disconnect the battery with the engine running. That's a real easy way to do a lot of expensive damage. That was a test done many years ago by mechanics who didn't understand how these simple systems work. All AC generators develop "ripple" voltage. The battery smooths that out which eliminates the problem it can cause. If you want to tell if the generator is working, use a digital voltmeter to measure battery voltage while the engine is running. It must be between 13.75 and 14.75 volts.

If the generator has one defective diode out of the six, you will lose exactly two thirds of its output capacity. Ripple will also increase greatly. That can cause the symptoms you described, especially at idle where maximum output is going to be even lower. I'd start with a load test on the generator. Most professional testers display ripple as a bar graph, not a number. If ripple is high and maximum output is around 20-30 amps, suspect the generator.

If the engine is not idling at optimum efficiency, the problem can occur. It is not necessarily electrically related though increased draining of electrical power can cause it.

Improperly adjusted ignition timing and valve clearances are possible causes,

Did you clean the throttle body while rlacing the TPS and IAC?

I think there might be some confusion. The generator is not perfectly fine if the voltage dropped to 12.5 volts. Unless the belt is loose, that sure sounds like there's a bad diode in it.

The load test you need to do is with a professional load testing machine. It will draw the maximum current your generator can deliver while maintaining at least 13.75 volts. By turning on the lights and AC, you were doing a similar test but the generator should have easily kept up with that minimal demand.

Your generator is rated at 80 amps. If one diode is defective, you will lose exactly two thirds of its capacity so about 25 amps is all you'll get. Head lights, tail lights, and the heater fan will draw around 20 amps leaving not much left over. Once that capacity is exceeded, voltage will start to drop.

One other thing to consider is generators are less efficient as they slow down so load tests are always performed with the engine at 2000 rpm. If you made your observations at idle, you may not have a generator problem although the voltage still shouldn't have dropped that low.

It also sounds like you might not be understanding exactly what "ripple" is. It has nothing to do with engine idle speed as your comment suggests. It is the variation in voltage developed by the generator. For a better explanation if ripple, look at the bottom of this page under "Excessive Ripple":

http://randysrepairshop.net/charging-systems.html