For me, it may be that the toilet paper roll needs to have the open end away from the wall. I don’t want to reach under the roll to take a piece! That’s ludicrous!
That or my recent addiction to correcting people when they use “less” when they should use “fewer”
This is what I was thinking of, which does have two snakes and a stick in it. https://en.wikipedia.org/wiki/Tiresias
That would be more similar to the Caduceus anyways given the number of snakes.