Woke up this morning and noticed black, watery liquid coming out of the thermostat and dripping down the wall. Took the cover off and noted that the liquied is coming out of the shared, wire sheath (that all the wires are in as it goes back into the wall). The heating continues to work just fine but I have never heard of, let alone, experienced this. Any ideas, clues, suggestions?

It's a Ritetemp digital; initially I thought it was one of the back up batteries leaking acid but confirmed that is not it.

Sounds like some sort of a water leak. Water can pick up black from the roof or something. Does this cable go up or down? I would go to the other end, and look for a problem there. I just don't see watery black liquid developing within a cable. I guess it could enter somewhere the sheath is damaged. More details on your system would help, a condensing furnace in the attic?