Pink elephants

What exactly is the origin of the term “pink elephant,” how old is it and what exactly does it connote? I was only aware of the drunkard’s hallucination commonplace, but I’ve seen it come up in more philosophical discussions (epistemological and language arguments and sometimes in political talk)-- the meaning or implication seems to shift (sometimes it seems used in the same way as ‘white elephant’ but it could be that the authors are confused). What’s the original context? Any ideas?

No idea how old, or what origin. It tends to be used as an example of something that could exist, but for which there is a total lack of evidence, therefore no reason to believe in it.

For example:

Theist: you haven’t proven that that my God does not exist, so why do you think he doesn’t?

Atheist: I haven’t proven that pink elephants do not exist, so do you think I should believe they do?

I think though that the concept is used in various ways.

Surprisingly the phrase only goes back in print to 1940.

I think that the phrase meant both the drunkard’s nightmare and the impossible thing to imagine that Princhester suggested.
I think it more likely that today’s idiom is a “pink unicorn.”

Hmm. The Disney film Dumbo (you remember the pink elephant sequnce, right? Brilliant) came out in 1941, so either that was the origin of the trope (unlikely) or developed in visual culture with no printed descriptions before that? Samclem–was that 1940’s print appearance an OED cite? I wonder if it comes from another language. . .
This gets more puzzling.