The caster of detect magic will see a faint aura around the person who has the magic item
It doesn't matter where on (or in) their person the magic item is.
The spell says:
For the duration, you sense the presence of magic within 30 feet of you. If you sense magic in this way, you can use your action to see a faint aura around any visible creature or object in the area that bears magic, and you learn its school of magic, if any.
The item need not be visible, only the bearer
You will note the magic item need not be visible, only the "the creature or object . . . that bears [the] magic".
In your case the person with the magic item is visible, and within 30 feet. The caster sees the aura.
You can't tell where they've hidden it from the aura, only that it is on (or in) their person and not visible itself
It doesn't matter where about (or within) their person the person in your example has secreted the magic item, they are outlined. Furthermore, the caster cannot tell where. The target might have the item on a hidden necklace, in a pocket, under their hat, or it may be in their mouth, or they may have ingested it, or it may be any number of other places. The only thing the caster knows regarding location is that the item is hidden from view, otherwise the item itself would be outlined.
The barrier clause is not applicable in this case
The spell further notes:
The spell can penetrate most barriers, but it is blocked by 1 foot of stone, 1 inch of common metal, a thin sheet of lead, or 3 feet of wood or dirt.
We assume in this case none of these apply, but if the item were wrapped in lead foil and then the person hid it about their person, it would not be detectable.
What about answers arguing to the contrary?
This answer argues the contrary. The difference is interpretation of the phrase "creature or object in the area that bears magic".
The answer interprets that phrase to mean the item itself, I believe the correct interpretation is that of the person or object who possesses that magic object.
Furthermore, if the item had to be in sight then there is no reason to include the sentence "The spell can penetrate most barriers...." if in fact it only penetrated transparent barriers.
Other ambiguities
All vs. any
To my reading, the phrase "any visible creature or object in the area that bears magic" could be misread that only one creature or object is outlined. Perhaps the writers hewed to some style guide instead of writing for clarity: "all visible creatures or objects in the area bearing magic" would have been clearer.
Multiple magic items
Apparently the writers of the spell never actually met any PCs. Every one I met that had been adventuring for more than a hot minute would light up like a neon sign with multiple items (tbf, most NPCs too); yet the spell does not account for showing multiple auras. However, assuming each item produces its own aura about its bearing entity resolves the ambiguity.
