Battery dies when it rains

I have a 2002 Honda Civic HX. In rainy weather, I have been finding that I have a dead battery when I go to start it in the morning. It needs to be parked overnight or longer for this to happen. When I drive in wet weather, even through puddles, there are no problems. The battery was replaced in May, and the problem preceded that, so I am fairly certain that it isn’t a factor. After a jump start the car will run just fine until the next time it sits unused in the rain. My hunch is something to do with the spark plug wires as those are old and I know can cause issues in wet weather, but I’m not sure that can explain why the battery drains.

Another potentially related issue is that the cruise control will sometimes turn itself off. It doesn’t just disengage, but the whole system turns off. I haven’t totally correlated this to use in wet weather, so I’m not sure it is a factor. It was definitely a wet day when it was doing it the worst. I’m less worried about this issue and am just mentioning it in case it is related.

Any ideas? Thanks.