Gonna have to get down to closer looking than the info we currently have. Wet weather outside should not change things inside,s o we are getting confusion?
Some random questions that are in no particular order of importance.
Do they go out when the wipers are running and come on when not, or is it simply driving in wet that might indicate a major opening letting water get in? There are a multitude of "possible" things but I might first guess that it is a loose connector but odd that it comes and goes but we are left guessing without more info.
How to fix it?
I would first go into deep study of when it is out and when it works again and try to pin down a cause of failure and fix. If the wipers running put it out, I look at the mechanical links to the wipers to see that they are not snagging some cable. If it is an opening letting water into the works, I look for that.
Assuming is dangerous but I do it anyway! So assuming it is a cable connector that is not quite on, nor off and just kind of bounces around to make or not make connections, I would want to find a drawing for the dash electrical. Little things we don't know yet, like if the fuse blows, will be important clues.
Sorry for the non answer but we need more specific info.
I would first go to the drawings and find which connector feeds the
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