I never liked the idea of a axe inside the Jeep unless it was bolted down good. Nothing like you or your kids getting hit in the back of the head with a flying axe. I would mount it outside. It's a axe, doesnt really need protection from the enviroment.
I've seen someone that mounted an axe in the rear on the angled part of the roll bar. I'm not sure what he used to attach it or secure it but maybe you could mount it there and come up with a creative solution to attach it.
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