How do you parse "hair do"

Is "do" understood as a noun or verb in "hair do"?

Asking this in search of "to make do".

Bonus points if it can be related to German Tolle "tuft [of hair], that thing that Elvis had on his head", itself of obscure origin, surely under influence of toll "wild, great, fun".

En. dole doesn't seem to be a bad fit, either, as general as its cognates are (portion, piece, divide).

A hair-do (or hairdo) is a hairstyle. You have your hair done by a stylist and the result is a hair-do. In this case "do" is a noun.

A hairstyle, hairdo, or haircut refers to the styling of hair, usually on the human scalp. https://en.wikipedia.org/wiki/Hairstyle

"do" on its own can be a noun - https://dictionary.cambridge.org/dictionary/english/do

It is the way your hair is done; the way you do your hair (or others, such as hairdressers, barbers, stylists do your hair). Your hair do. (It acts as a noun phrase.)

I would venture that this ambiguous application of do is related to the word's catch-all etymology, including "make," "do," or "place."

Middle English don, from Old English dōn; akin to Old High German tuon to do, Latin -dere to put, facere to make, do, Greek tithenai to place, set

Or it could refer to some goo used to style hair like 'Hair Doo' or 'Kleenex.' Who the hell knows 🙃