UPDATE: Added a script to the Pip-Boy Glove which ensures that the player only ever will have one at a time.  If you do pick up another Pip-Boy Glove, say from a dead NPC who was wearing one, the script will remove it automatically.
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Okay, not as much explanation on this one, since it's a pretty basic mod.

Short version: this removes the tag on the Pip-Boy Glove that makes it not show up in the Apparel screen.  This means that you can equip or remove the Pip-Boy Glove whenever you want, just like any other piece of clothing.

So as not to screw up anything dependent on the glove, it has also been marked as a Quest Item.  This means you can't drop it, sell it, or transfer it to a container.  It also means that nothing can confiscate the Pip-Boy Glove from you, say if you have your equipment confiscated as part of the Dead Money DLC.

That's basically it.  You can now take off the glove when it would look better with certain pieces of armor, like the Chinese Stealth Armor or Radiation Suit, and then re-wear it if you later feel the need.


NOTES

Yes, I am quite aware that there are other mods which do this same thing, more or less.  However, mine is currently the only one that lets you equip and unequip the glove via the Pip-Boy menu which doesn't also let you drop it or require some extra textures/etc.  This is a blood simple mod that ensures nothing will get screwed up in the process, and as such should be very compatible with other mods.