I think it comes from the phrase “bats in the belfry”, but people who go into the caves to collect bat shit (it is actually called ‘guano’ & it makes an excellent fertilizer) warn that they have to wear masks in order to get the ‘guano’ out. They have to wear masks because the guano is both musty & dusty, & if they do not wear a mask, it can lead to hallucinations. So, ere-go – you have “bat-shit crazy”.
Just a random thought, could it have to do with the fact that rabies is fairly common in the bat population and has been known to be transferred to humans? Is the crazy part more to do with the rabid, foaming at the mouth, psychotic symptoms of rabies?
Well, @ETpro , I think the ‘miners’ of the guano (bat shit) do not have very many alternatives to earn a living other than mining the guano for fertilizer. It is something that they have to do, in order to survive. I think, that if they had a viable alternative, they would not be ‘mining’ the guano!