Quick update on this.
I knew if the water stopped in the spring it had to be a moisture issue from inside the chimney. It did, issue confirmed. So I started the task to get a new water heater and vent it differently.
I knew my chimney had a nice flexible liner in it from a good company since I had the bill from the previous owner and had talked to the installed of it from 7 years ago. The bill said hooked to furnace.
Well people don't assume anything. I was working down there doing some prep and pulled a few things out and realized the liner is actually hooked to the coal stove. I talked to the chimney company and he verified that this type of coal stove in this configuration they would very well refer to that as a furnace on the bill.
So now back to square one in the fact I don't know if the moisture / condensation is caused by the furnace, water heater or most likely both.
I ended up having the chimney company come and disconnect the liner from the coal stove/furnace and pull it right out and seal up the coal stove hole (cleaning the stove up now to sell). They turned the liner, cleaned it, and hooked both the NG furnace and NG water heater to it. Sealed the extra hole on the top of the chimney (the one that was just open to the cavity), insulated it all and it looked great.
It was a little bit more then buying a direct vent water heater, but I might have done all that and still had the problem if the furnace was more the issue.
Now I can go up in the attic when it is a bit cooler and scrub the chimney down to hopefully get rid of all those dark drips and stains.