Narrowly addressing the original question, you can say "Good luck on your new job" or "Good luck with your new job" but you cannot say "*Good luck for your new job." As shown above, "for" can only be used when the expression is not a wish.
I claim the distinction between "on" and "with" is that "on" wishes luck over a process while "with" wishes it on an outcome. Consider these cases:
"Good luck on that paper." I'm wishing him success writing the paper.
"Good luck with that paper." I'm hoping his teacher takes pity on him.
BUT, if he's en route to class, paper in hand, then they mean exactly the same thing because almost nothing is left of the process.
I can say "Good luck with your boss" to a person who's having trouble at work, but I cannot say "Good luck on your boss" because the boss isn't a process. I could say "Good luck on getting that raise" though.
I would claim, then, that the reason you can't say "Good luck with the campaign trail" because the trail cannot be an outcome.
I think it is a pragmatic side-effect that using "with" when I could have used "on" implies that I think the result is out of the control of the listener. Tone of voice can strengthen this effect, as in "Good luck with that."
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