So, here is what I hope to be a final resolution to this issue.
I polled every system on the car and came up with nothing definitive that would point to any particular problem. The car has been sitting in the garage with the back seat out since the day of the first post and everything is nice and dry now and the systems are behaving properly with the battery connected.
The only remaining mystery is the persistent red light on the tow button. I pulled the door lock pump from under the seat and began pulling the connectors off. Amazingly, the red light went out! I continued to remove the rest of the connectors and that's when I spotted the badly corroded pins on the two multi-pin white and black connectors on the end of the unit.
I removed the vacuum lines and pulled apart the pump and this is what I found:
(Sorry for the one crappy picture)
I don't think that happened all at one time but I believe that the combination of the spilled bottle of water and the cold rain aggravated situation to the point that things started acting up.
We plan on getting circuit cleaner and a toothbrush and cleaning it up to see if it solves the problem permanently.