I had the same issue with my TT. The pump would run randomly and moan now and then. Then I discovered that the check valve that is supposed to stop city water from going into the freshwater tank was not even installed. This is because there was a repair done by the previous owner and they did not re-install a check valve. so I was getting water in my tank without hooking it up.
I went to Lowes and purchased a check valve and installed it directly into the line the feeds off the pump. Problem solved.
See here what I mean.
My Video Here