Fan starts running with no witnesses

1980's Honda. The owner only drives maybe once a week due to age. New battery slowly over time runs down. Then they try to drive twice a week. There's a secret plan between car owner's daughter and AAA. Every time the car owner needs a new battery no matter how young the battery is, just replace it and they pay AAA for it, and let the car owner think it was an outdated battery and the cause is their lack of driving it. I have been called over there 2 times to jump the car and it starts right up. After the jump it starts fine that day and the next day. I'm not clear about all this car won't start scenario. The times I'm not called over being a relative of their's they deal with AAA. So now the cause of the battery running down is some mysterious fan issue. AAA and another relative of car owner who is very car mechanically inclined both say that some fan is coming on and running when the the car is not running. AAA will tow it to a shop next week to get a new fan. I spoke to the car owner and asked about this fan. What fan? They do not know. I said there's a fan behind the radiator and a fan for the heat and air conditioning blower. I asked if they and AAA or the other relative were standing there with the engine off and saw the fan running. They said no. They said they all heard it running but won't raise the hood to look. The car owner trust AAA. What fan can be replaced that would solve this issue of the battery running down when the car is not running?

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