Voltage drop

Why would you think it is a pump when it could be a bad wire connection or a bad relay?

And why replace the expensive pump when a length of wire can confirm?

Go to anyplace that sells any wire. Look up the pump specs Determine the size wire it needs for the power. Buy say, 20' of wire that is at least one size larger than needed. Wire it temporarily direct from the battery to the pump. If it seems problematic, obtain a multimeter that can handle the pump current and measure it's current draw.