[Clifton]

There are few threads on here RE: battery replacement and water pumps that discuss strange runaway water pumps after a battery replacement.

For lack of better terms, the Water pump is wired outside of the normal key'ed power so that it can run to cool engine after you've locked up and walked away.

The down side to that is if you don't follow battery replacement procedures, you can short the water pump causing the run away effect leading to high battery drain.

Not saying this is your issue, but sounds very similar given both cases you mention connecting the battery.