We are going to need a little more info and/or some pictures as some of what you mentioned seems confusing.
You mention your outside shower has never been hooked up?
Does that mean you never have used it or they didn't hook the plumbing to it from the factory? If you've simply never used it, you might take a look at it anyway. Sometimes the valves have a way of vibrating open slightly and it will drip inside the compartment and then leak inside the camper when the plumbing is pressurized.
You also mention your pump might be leaking. Is it located in the sink cabinet? Pumps can leak (somewhat rare) but if it's located elsewhere other than the sink cabinet then probably not the pump.
Outside black tank flush plumbing often has the back flow check/anti-siphon valve located in the bathroom sink cabinet and more of those seem to leak than do not.
Give us additional information, otherwise we are just guessing.
2016 Flagstaff 8529IKBS Diamond Package 5th Wheel
Ford F-Series SCREW 4x4
TST Tire Monitor - Sinemate 3500w Gen.
2016 Nights Camped = 44