It seems more likely to me that only the girls where stripped and he just whipped out the "root cause" from his fly.

Painfully that was somewhat true in the 18th century, when rich patrions would obtain sexual sevices from the (very young) ballet girls.

♫ Long Long Man ♫ (Sakeru Gummy)

You almost got it right. The proper meaning is "Girl who blows in the ashes to rekindle the fire"