Hi,
These vehicles are very sensitive to low voltage. The idea that the RPMs increase when you apply an electrical load leads me to think it is running off the alternator only and the battery has shorted internally.
So, the first thing I want you to do is first, check for battery voltage at the battery using a voltmeter or multimeter and let me know the voltage.
If the battery checks good, and I suspect it won't, next make sure the battery terminals are both clean and tight. If they are, jump-start the vehicle and check the voltage at the battery with the engine running. It should be around 14v.
Here is a link that explains how this is done to test an alternator:
https://www.2carpros.com/articles/how-to-check-a-car-alternator
Let me know what you find. Also, it's important that the battery terminals are clean, tight, and free of corrosion, so make sure they are good.
Let me know the results so I can explain what to do next.
Take care,
Joe
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Wednesday, November 9th, 2022 AT 8:26 PM