Question: In your game, a character discovers a Gauntlet of Ogre Power. Not Gauntlets, Gauntlet. One Singular. Let's say it fits the right hand. How do you rule? What is the effect?
I'm confused. On page 217 of the Dungeon Master's Guide, there is a side bar titled, Magic Item Rules. In that sidebar, there is a paragraph on "Paired Items".
"Paired Items. You can allow exceptions to the rule that paired items must both be worn. For example, a character with only one arm might be able to use a single Glove of Missile Snaring so long as the matching glove is on their person."
There is no example of one item of a paired set still being used, attuned to, or being able to deliver some magical benefit to the wearer without the other item in the pair.
That does not mean that the owner of this gauntlet cannot use it to scry on the location of the other glove in the set, or that they can't somehow find the other gauntlet in the set. It may be entertaining to put the other gauntlet in the set in a gelatinous cube, or stuck on the side of a rock ledge, over a pit of acid, for instance.
Now, I think I could see an instance where a pair was worn by an adventurer, and perhaps one of the gauntlets were destroyed, while the other was not. An example would be a fighter was pushed over a ledge, and the party grabbed one glove, which slid off his hand, and he fell into lava, acid, or some other such substance that destroyed the other glove.
Now, in this instance, I may allow the surviving gauntlet to be made into a x/day or Proficiency Bonus times per day item, if the player takes it to a wizard, artificer, or some other magically inclined person and had as much of it repaired or mended as possible. I would not call this new item a gauntlet of ogre power. I would instead rename it after the PC that is now wearing it, and it would be a "unique" to the campaign item.
I would not allow the found item to have any inherent or innate magic item bonuses or abilities all on it's own, especially when it started out as a part of a set. I would encourage the player who found the item to learn as much about it before I offered up any of the additional options I wrote about above.
In effect, this item would be a sub-plot thread that the player(s) can pull on or not. It would be entirely up to them.