Why did you replace it? Was it in an attempt to solve the erratic gauge, or some other problem?
I should have also mentioned to check the various ground wires for rust or looseness, especially the smaller negative battery wire that runs from the cable clamp to the body sheet metal.
The symptoms you described can be caused by a perfectly good, but aged battery, which I already described. In addition, when you have an electromechanical instrument cluster, the generator's internal voltage regulator monitors system voltage right at its output terminal, but when you have a digital dash, its brightness is very susceptible to tiny system voltage fluctuations, so they use an additional wire in the generator's small plug to monitor system voltage right at the dash. That is done to maintain the supply voltage perfectly steady there. Any minor fluctuations won't be noticed in other vehicle systems such as the power seats and radio.
Voltage fluctuations can also be caused by a failed diode inside the generator. The voltage regulator has to fight to hold output voltage steady and usually doesn't do a good job of that. Most charging system testers, other than the simple hand-held style, include a diode test as part of the load test. A few models actually print it out as a voltage, but most just use a relative bar chart to show "ripple voltage" between "low" and "high". All generators put out a little ripple voltage, but that goes a real lot higher when one of the six diodes has failed. The voltage regulator looses control of system voltage when it tries to keep up with this varying output voltage.
The additional clue to a failed diode is the generator will develop exactly one-third of its maximum rated current under the full-load test. The standard generator for your vehicle is a 120-amp unit. With one failed diode, the most it will develop is 40 amps. Forty amps is what some older generators were capable of, so some testers will interpret 40 amps as "good" under the full-load test, but it's 120 amps you really want to see.
If your testing did get close to 120 amps, we can rule out a failed diode. That would again point to an aged battery or rusty ground wire connections.
Another test is to unplug the generator's small plug while the engine is running, then observe if the erratic gauge becomes steady. If it does, we know this is related to the generator and battery. If there is still unstable voltage fluctuations, look in a different direction, mainly the ground wires, but also the 12-volt feed circuits. Loose or corroded fuse terminals and mating connector terminals become good suspects for that.
Keep in mind too someone could have previously rerouted a wiring harness, especially on the engine, and that could place some vulnerable wires in pulsing or varying magnetic fields from other wires they aren't normally supposed to be near. This has been especially common when those generator's voltage spikes interfere with computer sensor circuits.
Keep me updated on what you find, then we'll figure out where to go next.
Saturday, December 26th, 2020 AT 5:22 PM