Explain please. What do you mean by flicker? Are the lights switched on at the time and flick once when the pump starts and once more when the pump stops, or do you mean they flicker into life when they are switched off and the pump starts.
If it is the former it is caused by the relatively large current drawn at the instant the pump starts this current creating a brief voltage drop across the battery (which suggests your power supply may not be working correctly as it should be able to source that current demand.)
If the lights flicker when they are switched off the only possibility is current being induced in lighting wiring from close/adjacent/co-wound cables that are carrying the much higher pump current.
A varistor or Voltage Dependent Resistor is a semiconductor device that draws almost no current below its rated trigger voltage, but go above the trigger voltage often by a relatively small amount and it can instantaneously pass hundreds if not thousands of amps (we are talking a few microseconds here.) They are the devices fitted inside mains extension blocks that stop high current pulses damaging connected devices. Once you know the spec or type of VDR you need they cost pence, certainly well under a pound. I do not understand why a dealer thinks this will cure the problem. Maybe it just makes him sound good?