This now points to something in the distribution box broken or cracked or something kooky in there. There is a drain for the water A/C makes normally and it too may play a part now. They can clog and A/C "condensate" it's called needs a place to go out and not on the floor. Most are a rubber elbow towards center, lower, engine side of firewall. It must be open. Perhaps if you find it you could blow some compressed air in it (gently) and see if it goes thru.
Other than that a look while standing on your head up under the dash while it's doing it may show the source. I'm a little confused why this is doing this when you ask for heat and not just anytime it's wet out or snow or ice melting no matter what is on or off. Do you find it wet when the car is not being used at all? Windshield leaks can do this but they shouldn't care about what you are doing for heat at all.
The one side being warmer than the other could be that there a lot of muck in the box or a poor connection of ductwork that may be like a dryer vent peice of tube or a plastic job.
Gonna have to look as best you can. Sometimes thru glovebox can help,
T
Tom Greenleaf - MetroWest Boston - USA
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