As others have said, there is only ONE place fresh water can make it into the black tank, the nozzle in the top of the bowl flush. If that isn't leaking continually into the toilet, there's no other way fresh can get into the black tank (unless gremlins are sneaking in and using your toilet.
).
Your pump running can be many other issues. A leaking water line, low point drains dripping, dripping faucet, outdoor shower not completely turned off. Need to do some detective work.
Another thing, the indicator lights for tank levels are VERY inaccurate, so don't always assume they are correct.
Lastly, did you put a "Y" splitter on your water line and have it connected to the black tank flush fitting? If so, that could be leaking into the tank.