I don't know what the "rules might be" (I am Novus Ordo as a registered parishioner and weekly Mass attender according to the 1969 Roman Missal in the Diocese of Spokane, WA ... just mentioning this for context), but I'm also OLD, born in 1951, First Communion in 1959, Confirmation in 1964, both according to the the "traditional sacramentary". Some "remembrance" recalls that perhaps we were the last class confirmed from that Sacramentary as I was an altar server for my parish's Confirmations in 1965 and things were different: still all in Latin, but Confirmation occurred within Mass rather than outside of it, and the ceremonials were simpler.
Anyways, I do recall "growing up, and attending parochial school" in the 1950's and 1960's in eastern WA: Women wore hats or head scarfs back then rather then what is today viewed as "the veil". Babies and very young girls wore bonnets. Older girls, and my contemporary parochial school classmates, often wore something I've not seen depicted often recently but it was a "lace like" (for lack of a better description) piece that covered the top of the head but did not "protrude" or "flow" down the side of the heaD, and generally held in place with a "bobby pin". Parishes often had a "box of these and bobby pins" in the narthex. At school day Masses a Sister would always be in the narthex with a box of tissue and some bobby pins in case any girl was missing her head covering.