I can't seem to find an origin to this particular phrase.
Can anyone shed some light on what makes sh*thouse rats particularly crazy?
I also wonder about the origin of the similar *Bat-shit crazy".
My suspicion is that someone coined them both because they sounded funny, but I was wondering if there was a better explanation?
There is also another slightly different version of this phrase, which is believed to pre-date your version:
Nuttier than a sh*thouse rat.
also
Nuttier than a sh*thouse mouse.
It is intended as a pun on nuttier, since nuts are hard to digested they are likely to show up in the feces - which obviously end up in the sh*thouse. Since you can also be "nuts" I believe it changed later to "crazier".
I've always been taught that "batshit crazy" originated because bats are disease carriers, and that prolonged exposure to their guano makes a person nuts. Now, to back that up.
First, the CDC recommends avoiding bats because they have been known to carry rabies, which in and of itself is bad, but there have also been new discoveries recently that bats also are carriers of a whole host of other things, such as hemorraghic fevers, lyssaviruses, coronaviruses, and a variety of other lovely things that tend to affect your brain. They are also known to be carriers of histoplasmosis, which can be present in their excrement. It's generally not a good idea to expose yourself to bat poop, although apparently it makes a good fertilizer.
As for the shithouse rat, I've got less on that. Seems like a lot of people on the internet tend to assume the original is "nuttier than a shithouse mouse", because apparently mice would eat nuts and thus excrete bits of nut, and where better to find piles of nuts excreted from mice but the shithouse?
It's also been suggested that it is not the shithouse making the rat crazy, but the sheer fact that the rat would live in the shithouse instead of somewhere less, well, crappy, that makes the rat crazy. I can't, unfortunately, find definitive backing on these, short of a lot of people in a lot of random forums saying that is what they think.
As for batshit, OED suggests that the term is a derivative of apeshit, which predates it. The entry at apeshit refers to a 1961 article in the journal American Speech (36(2): p.150), the relevant part of which I quote below:
Perhaps other parents have had the shock of hearing terms which we knew to be vulgar used by present teen-agers but with none of their earlier scatological meaning. No doubt the most common of these terms is chicken, often heard in reference to the deplorable games of daredevil young drivers. It seems likely there were two sources for this term, causing some of the present confusion of meaning. One source is the old terms chicken-livered and chicken-hearted (Middleton used chicken-heart in 1602, according to the OED), giving the meaning of cowardly; of course, the games of chicken, one of which is to let a car run without hands on the wheel until one passenger panics and grabs the wheel, are supposedly games or tests of cowardice and bravery.
But the more earthy source for chicken has nothing to do with cowardice, and this meaning was a commonplace in the thirties and forties. The word was usually heard adjectively in three syllables, combining chicken with the vulgar noun for feces. This meaning of chicken, then, was one of general condemnation and disparagement, but with no reference to cowardice. It is this meaning that one hears in the classic old Army sentence used by the comedian George Gobel on his television program on February 28, 1960, when he asked: 'How do you get out of this chicken outfit?'
A similar small fog seems to exist around the term gone ape. To the younger set, it implies behaving in a wild, irresponsible manner. As used in Time in the issue of August 24, 1959 (p. 64), the phrase gone ape described a Jacksonville, Florida, radio station (WAPE) which uses the recorded voice of a bull ape in its station breaks. The older implication would seem to be that of the wild and panicky actions of apes and other wild animals when captured and caged. They will often mark up the cage or room with their feces as they dart about the enclosure in panic. The exaggerated, unflattering connotation of wild, self-dirtying activity was ascribed to individuals or organizations that had gone ape during the Second World War, but this older meaning seems to have disappeared.