willy-nilly

Literally, “Be one willing to, be one unwilling to”. From will I, nill I (“whether I want to or not”, with both verbs in the subjunctive), reflecting the old (viz. pre-Great Vowel Shift) pronunciation of I as ee, not yet as eye. Conflated with will he, nill he (with silent h) and will ye, nill ye (with yod dropping), meaning likewise “be he/you willing or not”.

For more, refer to the individual component words:

will (“to desire, to wish, to be willing”) (archaic)

nill (“to not desire or wish, to be unwilling”) (obsolete)

Compare Latin volens nolens, velim nōlim and English harum-scarum, which have this same meaning.