Electrical leakage when rains

[tomo]

During the recent rainy days my cougar stuttered pretty seriously (twice). It seemed like some electrical problem. Spark plugs and wires are almost new. When I turned on the rear screen heater all the lights dimmed a bit. I noticed the right headlight bulb got burnt, I replaced it and 3 days later it was gone again. When it’s dry everything is fine. Any ideas what it could be?