The symptom makes it appear to be dirty power. Spikes causing the failure. But the relay cleans that power circuit to the ballast.

Only thing I can think of - where did you source the power for the ballast relay? I know you said battery, but was it your own wiring or did you pickup a master feed somewhere else?

Other thing that is a vague kind of possibility. Battery failed and was replaced. Why did the battery fail? I know you said the alternator is putting out a good charge, but how do you know it's a stable charge and not spiking? Rhetoric question really, because it's difficult to monitor it sufficiently to analyse. And if it's outputting a variable voltage (spiking), why isn;t it frying other things?

I know, asked and answered my own questions, but I feel that sometimes these kind of brain dump discussions can help the OP work towards a solution.

Good luck with it bloke.

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Cheers,

Anthony