Moisture can really throw a wrench into electrical systems, causing all sorts of trouble like shorts and corrosion. So, I suggest checking all electrical connections, especially the ones that are exposed to the elements like connectors, wiring, and the fuse box. Look for any signs of water damage or corrosion.
Another thing to check is the grounding. Sometimes wonky grounding can cause the symptoms you're seeing. Make sure all those connections are clean, tight, and not rusty.
Also, it's a good idea to double-check your battery and charging system. A weak battery or issues with the alternator or voltage regulator can cause electrical problems.