If you can possibly manage, it would be instructive to measure the voltage drop in the power and ground lines to the pump. Simply hook the meter up between the battery positive terminal and the pump's positive, and then likewise for the negatives, both with the pump operating. It would be okay to use a wire to extend the voltmeter leads; the voltage drop in the sense wire will generally be utterly negligible for this sort of check as the current flowing through the voltmeter is on the order of microamps.
I haven't measured mine (nor have I had any reason to suspect I need to), but a 3V drop in the wiring to the pump is certainly neither normal nor acceptable.
On my RV, and maybe on yours, the wiring to the pump is rather extensive as the various switches to turn it on and off are all inline with its power lead. I happen to have two such switches, one by the outside shower and one on the inside, wired basically like a two-way switch for a hall light. I don't have a separate pump controller module with a relay as is sometimes done.