Where did the phrase "batsh*t crazy" come from?

This might be a stretch, but what the author says here makes some sense.

However, it was interesting to note the first recorded usage of each of the elements of the phrase: bat appeared as bakke in C.E. 1340; shit appeared as schite in C.E. 1308; and crazy appeared as crasie in C.E. 1583. Knowing as we do that a) modern English words beginning in sh or sch began life as Scandinavian words beginning in sk, and b) bakke, with its hard b and double k, is obviously also of Norse derivation, it wouldn’t be too improbable to guess that Vikings were running around Northern Europe describing last night’s pillaging as totally “bakke-skite.”

The term has on occasion been attributed to Hunter S. Thompson, who was a lover of bats and quite crazy in his own right, but I believe the term originated well before Thompson's time.

The word crazy is a later addition. Scanning Google Books I find a handful of references starting from the mid-60s where batshit is clearly just a variation on bullshit (nonsense, rubbish) - which meaning still turns up even in 2001, but it's relatively uncommon now.

Here's a relatively early one from 1967 where the meaning is crazy. A decade later most references have this meaning, but the earliest actual "batshit crazy" I can find is this one from 1989.

I'm not sure it makes a lot of sense to call batshit a "euphemism" for bullshit, but it does seem to me that's how the word got started. In ordinary speech there's no meaningful difference between "That's bullshit!" and "That's crazy!". Bats in the belfry/batty had been around since 1901/1903; obviously people just latched on to that crazy connotation, thus popularising the word-pair.

From an inexplicably deleted answer is a 1983 cartoon by P. S. Mueller (the voice of Onion News Radio) captioned:

Full blown batshit crazy and still holding down a productive job

Mueller adds:

Since I first published this cartoon around 25 years ago, I have received more correspondence about it than anything I have done before or since. I guess it struck a chord. As far as I knew at the time or know now, the phrase "Full Blown Batshit Crazy" just sort of fell out of my head and appears to have entered some part of the language. I seem to have the dimmest memory of a guy I knew in my early teens uttering the word "Batshit" on the school bus and nearly killing me with it. I could have it all tangled up with another guy or made it up myself, but it certainly sounds like something Birdy would have said.

I'm not sure when Mueller was born, but he "began contributing drawings to the Daily Egyptian at Southern Illinois University-Cabondale" from 1967, so his early teens batshit memory was probably around the early 1960s.

While looking up cut up rough, I detoured into going postal and run amok. Wikipedia goes into the medico-cultural (or perhaps culturo-medical) associations of the phrase run amok and links it to such phenomena as The Jumping Frenchmen of Maine (I kid you not), latah, and, wait for it, bat-schi in Thai culture.

If the phrase bat shit crazy originated in the era/area of the Vietnam War, perhaps it was because some GI had encountered bat schi in nearby Thailand.