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no matter how young the battery is, just replace it and they pay AAA for it, and let the car owner think it was an outdated battery and the cause is their lack of driving it.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?

Added (1). The car owner said the mechanic bill was $55 and the issue was some wire not connected. I think they told me the other day that when the key was turned they got nothing. That sounded like a dead battery or bad connection to the starter. Since the battery was not it I think then it must have been a starter connection or some other wire

It's not the fan causing the battery drain. You're correct, there are two fans in the engine, one for engine cooling and the other, a back up to help cool the engine when the AC is on. On certain models, after parking and turning off the engine, one fan (or both) will remain on to cool the engine. I had a friend who had this problem and I found it to be his alarm system shorting out from somewhere causing the drain. Disconnect the alarm, problem solved. Might want to check other locations too.

It would help to know what year and the actual model. In the late '80s Honda added a cool-down phase to the radiator fan. That circuit is fairly well known for turning on when the car is off. With the year and model I bet somebody here can tell you where to find the relay and maybe even the sensor responsible. Replacing the fan itself will not help at all; the sensor is going to be the likely cause.

The proper procedure is to remove a battery cable and place current meter between the connections to confirm a current drain. They are quite loud so anyone would hear it if it were on. If the fan were on it would drain the battery dead by the following day therefore it must be something else.