Battery voltage gauge not working properly?

Sounds like the gauge is working exactly as it's supposed to work. It's telling you what the charging system is developing for system voltage.

All generators are inefficient at lower speeds, so it is common to see system voltage drop at low engine speeds, especially when a number of loads are turned on, meaning things like the heater fan, head lights, and things like that. When the system is tested professionally, one of the requirements is we raise engine speed to 2,000 rpm during the "full-load output current' test. Your generator would not be able to pass this test with the engine at idle speed.

Check out this article first:

https://www.2carpros.com/articles/how-to-check-a-car-alternator

This shows testing the charging voltage with the engine running. It should be between 13.75 and 14.75 volts. If that is what you find, it only means it is okay to perform the rest of the tests, but that requires a professional load tester. The next test it will perform is that "full-load output current" test. The most common generator for your model was a 105-amp unit. During this test, one of three values will come up. If there's no defects, the tester will be able to draw very close to 100 amps. If the charging system is totally dead, you'll get 0 amps. The third possibility is to get exactly one third of the maximum rating, roughly 35 amps.

All "AC generators" develop three-phase output that is rectified into DC voltage that can be stored in a battery. That involves using a minimum of six "diodes". Diodes are one-way valves for electrical current flow. When one of the six fails, you'll lose two thirds of the generator's current-producing capacity. 35 amps can keep the engine running, but it is not enough to meet the demands of the entire electrical system under all conditions, and keep the battery charged. The battery will have to make up the difference as it slowly runs down over days or weeks. This lack of full output will be much more noticeable at lower engine speeds.

Along with the reduced output current, the one missing phase of the three results in very high "ripple" voltage. Professional charging system testers also test for this. A few models that can make printouts actually list ripple voltage as a voltage, but most testers simply show it on a relative bar chart according to the number of lights that illuminate out of typically five or six. We're only interested in whether ripple voltage is low, (normal), or high. High ripple voltage and a maximum of 35 amps both point to a failed diode, and both are normally seen at the same time.

I made this drawing to show ripple voltage. On the top waveform, each of the three phases takes a turn at producing some output voltage and current. The voltage is shown here. The difference between the highest and the lowest voltage developed is only 0.5 volts. With one dead phase in the lower waveform, ripple voltage is 5.2 volts, along with the full-load output current test only being able to develop one third of the generator's rated current. Besides not meeting the needs of the entire electrical system, a clue to this condition is an irritating whine on AM radio that changes pitch with changes in engine speed.

With the missing phase, and the generator's inability to keep up with demand, system voltage will drop, and be much more noticeable at idle. You'll see that as the head lights changing brightness along with the gauge reading going up and down as you change engine speed. This will show up on the voltmeter too if you measure battery voltage while a helper changes engine speed.

Start by measuring the battery's voltage at various engine speeds and tell me what you find. If you have the professional charging system test done by your mechanic, ask to receive a list of the results, then we'll figure out where to go next.

I should mention too that along with those three possible full-load output current results, if you find it to be somewhere in between, that can be caused by a slipping drive belt. We don't see that very often anymore with serpentine belts. Usually other symptoms, like loss of power steering or a belt squeal will show up first. Slipping belts today are often caused by a spring-loaded belt tensioner pulley that's rusted tight and is not putting enough tension on the belt.

Please keep me updated on your progress.