Here's a bit of thread necromancy from me as I just encountered an interesting archaic alternative to "willy nilly" fairly recently that I wanted to share.
I thought it might be interesting to not only know the Latin origin (from #3), but also to know that there are a few variants of "willy nilly" that can be found in literature. This is the one that I stumbled upon just today:
"We can give no other reason for [the storms at sea], but that it is a piece of its civility, that those that come among us may stay whether they will or no, and be copiously feasted all the while with the incomes of the ringing. Therefore pray to not think your time lost; for, willing, nilling, you will be forced to stay (...)."
[Background information: Pantagruel and his company visit the Ringing Island via ship and are 'forced' to rest there for a few days due to the rising storms at sea that threaten their voyage.]
While double-checking whether this particular usage ("willing, nilling") is perhaps idiomatic for the translator of Gargantua and Pantagruel I found the following site that lists a few variations from sources that span from Old English texts like Aelfric's Lives of Saints from [ca. 1000], to Shakespeare, to a plethora of sources from the 18th and 19th century. For anyone who is interested:
Here's some bits and pieces from the site:
"wille we, nelle we" (Old English)
"will I nill I" / "will you, nill you" / "will he, nill he" (modern English, but archaic)
"willy nilly" (a later variant of "will I, nill I...")
And apparently the phrase "shilly-shally" (meaning 'undecided') is related to "nilly willy".
The site says that these phrases are a combination of "I am willing" and "I am unwilling", which together was usually taken to mean "it doesn't matter to me one way or the other", but can also mean "whether you like it or not". The "haphazard" meaning seems to be a rather modern take on the phrase.