The title Gift of the Magi, is a biblical allusion from Matthew 2:1 reading: “Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem” (KJV). The Greek word for ‘wise men’ is Μάγοι (magoi) (plural form of μάγος (magos)) meaning a Magian, i.e. Oriental scientist; by implication, a magician:—sorcerer, wise man (Bauer 484).
You observed that her hair is twice described “like a cascade of brown waters.” Water—or waterfall in literature can often be symbolic of purity. The beauty of Della’s hair is compared to the natural beauty and purity of a waterfall ("cascade"). ‘Brown’ is an earthly color denoting ordinary, earthly quality it is the color of Della’s hair, her old coat, and her old hat—ordinary, well-used apparel. Compare to Jim’s need of “a new overcoat” and being “without gloves.” The extraordinary beauty of Della’s “cascade” of hair is juxtaposed with her ordinary garments—highlighting the richness (majestic quality) of her hair, “almost a garment for her”, compared to the ordinary clothing she wears. Della’s hair is more exquisite even that “Her Majesty’s jewels.” So, we have two seemingly ordinary people with extraordinary assets. Della with her hair that would make the Queen envious; and Jim with his watch that would make even “Solomon” (the richest king who ever lived) “pluck his beard with envy.”
And in context her hair is connected (as you astutely observed) to the motif of time denoted by Christmas (time), Jim’s watch, and the “[fastness]” with which Della’s hair will grow back: “My hair grows awfully fast”; “My hair grows so fast Jim”; “saving for months.” While the sacrifice of her hair is significant, it is not permanent—time will restore her beautiful hair—as she wisely observes. It is a renewable resource. Thus, her gift is “wisely” purchased, as it were—though arguably not practical from a realistic perspective.
Della also states “Maybe the hairs on my head were numbered” which is another biblical allusion from the gospels reading: “But even the very hairs of your head are all numbered. Fear not therefore: ye are of more value than many sparrows” (Luke 12:7, KJV). In context of the Gospel narrative, Jesus is reminding his disciples how much God loves them—God even knows how many hairs on our heads—and a fitting correlation of Della’s saccharine “quip” to Jim, “nobody could ever count my love for you.”
The motif of time grounds the story in reality—makes the reader conscious of time—and offers as you duly noted, an element of suspense. Additionally, we note the specific reference to time passing as "Within forty minutes her head looked a little better." Forty is a significant number. In the Bible, forty is found numerous times and is the number of completion—The Israelites lingered forty years in the wilderness and afterward entered the promise land (see Joshua 5:6); it rained for forty days before the flood (see Genesis 7:4); Moses was in the mountain forty days (see Exodus 24:18); Jesus fasted for forty days (see Matthew 1:13). Della’s forty minutes completes her transformation—perhaps from in some way extraordinary to completely ordinary--punctuating her sacrifice.
Another observation with the connection to hair, is that Della’s name is similar to Delila in the Old Testament—the woman who cut off Samson’s hair—the source of his strength—and was summarily subdued by his enemies (see Judges 16:4-21). As Samson’s hair was the source of his strength, Della’s hair in terms of her own perception, is the source of her beauty worried that her husband will pejoratively think of her as a “Coney Island chorus girl” and even praying, “Please God, make him think I am still pretty” as she has sold it (her hair) to purchase Jim’s Christmas present. But Jim proves his is not so shallow as all that when “He enfolded his Della” after his ironic revelation that he has sold his watch to purchase her present of expensive “tortoiseshell” hair combs.
As arguably impractical as these gifts seem to be of these “foolish children”, they are given sacrificially—each sacrificed their most valuable treasure—illustrating Jim and Della’s boundless (albeit perhaps impractical) love for one another. This is the theme of the gospels in which O. Henry has framed his story—“For God so loved the world” (Jn 3:16). The time motif also reflects squarely back into the gospel narratives of Christmas (or the birth of Christ) as being in the fullness of time: “But when the fullness of time had come, God sent forth his Son”
(Galatians 4:17 KJV).
Basically, the story depicts lives of seemingly ordinary New Yorkers who are as significant as any person of notoriety. These are ordinary people who give extraordinary gifts to each other—comparable to not only the gifts of the Magi (wisemen) who visited young Jesus—but to the wisemen themselves.
Bauer, Walter, et. al. A Greek-English Lexicon of the New Testament. University of Chicago Press, 1979.
The Holy Bible, Authorized King James Version, Thomas Nelson, 1972.