No need to buy a multimeter with long leads, just use whatever length of flex might come to hand, unless you are measuring critical resistance.
You may well measure full battery voltage across the pump supply and it`s ground with the pump unplugged, though that measurement is without the load of the pump in circuit, whereas while supplying the load that is the current draw of the pump, the voltage may fluctuate due to either a faulty connection on either the live or ground. In general ground connections seem to be those which cause the issues, that being the case, might be worth tracing to see where the ground makes it`s connection..?
Best of luck.
