Yeah, I agree - what I hear in the relay is definitely not a spark arc.
This is a mechanical "click", and spark arc is a definite "snap".

If he suspects wires, One thing he might try is grounding each wire solidly one-by-one, and see if anything changes (pull the wire off the plug and stick a screwdriver in it, and ground the screwdriver). If you have a leaky wire, it might stop arcing if you take the plug-gap load off it.
Then try floating each wire open one-by-one to see if it changes.
Might help isolate the offending wire.

DG