The narrator of "Gift of the Magi" is not a character, but he's certainly not a neutral observer either. Rather, he comes across distinctively as a person, and one who's telling you a story, maybe even at your bedside. He's willing to take breaks from the "action" of the story to paint a vivid scene. The narrator seems to speak directly to his "audience":
While the mistress of the home is gradually subsiding from the first stage to the second, take a look at the home. A furnished flat at $8 per week. (3)
The narrator also take breaks from the action to "make a point." He speaks as if he's seen the world and understood it well – he's wise, in other words – and he wants to teach you some lessons about it. Mainly on the nature of gift-giving, but he's plenty happy making short but sweeping statements about other things – like the nature of life, love, or women – while he's at it:
Which instigates the moral reflection that life is made up of sobs, sniffles, and smiles, with sniffles predominating. (2)
She got out her curling irons and lighted the gas and went to work repairing the ravages made by generosity added to love. Which is always a tremendous task, dear friends--a mammoth task. (20)
Although it might feel slightly heavy-handed at times, on the whole the narrator seems like a very gentle, well meaning, and wise fellow.