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The battery may need to be replaced if it is over 3 years old. It may be just low on water. Most places that sell batteries can load test them for you. IF you only have one battery (most dealers are too cheap to put in the two that are usually needed) then this may continue to be an issue. Hope that helps. Please get back to me if we need to dig deeper into the problem as all follow ups are included in our fee.
The battery may not be holding a charge and will come up shortly when the converter is kicking in on shore power. As long as you remain plugged in you might not notice it again.
Then the battery terminals may be dirty or that circuit may have a bad connection, especially a ground issue. Did you use a WFCO replacement or another brand. Progressive Dynamics makes about the best one and has adjustable charging rates. Get a small digital multimmeter and check the actual DC voltage at the battery when this happens.
Then time to do some actual testing on the DC voltages when this happens. Both at the battery and the light circuit.
As I first mentioned..........the battery needs to be load tested to be sure that isn't the issue. THEN, if that checks out, you can use a small digital multimeter to actually check the input DC voltage AT the battery........both when the shore cord is plugged in and when not. It should read a constant 13.7 VDC when plugged in an about 12.8 VDC when not. IF you see some fluctuations you know there is some kind of issue or possible short someplace. The light circuit can be checked as well. Both at the fuse and at the light. Process of elimination.
No.......and why not just have it load tested and find out? No use just guessing here.
NO............but, I would like you to do what I suggested and rule out the battery. I see this same question multiple times here every week. You asked for some help, but you seem reluctant to take my advice.
Not saying you are..........but, you don't understand how batteries operate and fail internally. They operate erratically when they are failing internally. Just a fact. I don't see this going anywhere so I will opt out of the question and allow another tech to offer something IF they can.
You didn't want to accept my advice about testing the battery. I an almost bet it is bad as you said it is over 3 years old. I have been at this many years and hold a Master Certified Technic***** *****cense. You shouldn't ask questions here and then not even attempt to do what is suggested and especially when it doesn't cost you anything. Testing the battery is free most places and a new battery would most likely solve this. I also told you how to check the system. Not sure what else you expected here. As for the fee.......have you been to a shop lately? Our fee is a great deal and one reason I answer over 2000 questions every year and still operate my own business!