willy-nilly

いわゆる"reduplication"と呼ばれる単語で、韻を踏むように繰り返されるのが特徴です。

"willy-nilly"の"willy"はお分かりのように"will"から来ており、意思のことです。一方、"nilly"という単語はないものの、"willy"の否定形と考えられます。

ここから、望もうが望むまいが、という意味に、また否応無しに、という意味になります。

Children with autism didn't benefit from an experimental therapy made with a hormone thought to promote social bonding, researchers reported Wednesday in the largest study of its kind.

"This is really a major setback," said Linmarie Sikich, a Duke University researcher who led the multisite U.S. study published in the New England Journal of Medicine.

（中略）

Larry Young, an Emory University scientist who does animal research with oxytocin, said it's too soon to give up on it for treating autism.

（中略）

"This is a very important study because it does say that just willy-nilly giving daily administrations of oxytocin is not going to lead to improvement," Young said.

(Lindsey Tanner. 'Sociability' hormone oxytocin didn't help kids with autism, study finds. Associated Press. October 13, 2021.)

行きあたりばったり、手当たり次第に、という意味でも用いられます。