The most likely cause of something like this is a faulty alternator that is not able to keep up with the load when the RPMs go up. Basically, when the engine revs up there is more of a demand on the electrical system and so the alternator will put out more voltage.
Here is a video on how to test the alternator. Basically, you need to perform the load test that is towards the end of the video.
https://youtu.be/Z-p4dMJUpUw
Turn as much of the electrical system as you can and then rev the engine and see what the voltage is. Basically, it may be able to keep up when it is idling because the demand is lower and so it can keep the battery alive due to the issue only happening a small amount of the time.
This will tell us if the alternator is keeping up with the demand or not.
Let's start with this test and we can go from there.
Thanks
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Monday, May 16th, 2022 AT 3:40 PM