So that you could briefly use another item without having it equipped so that you needn't reequip your constant effect items over and over.

I haven't heard of one. In the past, if I wanted to briefly equip an item so that its script runs, I have changed the ring/amulet item from type CLOT (clothing) to MISC (miscellaneous). You can see an example of how this is done with abot's Tempus Fugit ring mod. Basically when a misc item is equipped it does not force any clothing items to unequip, but its script can still detect that the user has equipped it and it can do whatever it needs to do. So, for example, this is a handy technique for implementing rings of teleportation so they do not unequip your CE rings.

Would that same functionality apply to normal enchanted items as well, or just scripted items? Not sure if there is much of a difference. :/

Just scripted, I think. But depending on what you wanted the item to do, it might be possible to operate via script.
Can you give an example of the kind of item you want to temporarily use?

If you want something like that for vanilla items, maybe you can make a mod that detects if your two CE rings are equipped. If one isn't then you wait a few seconds so you can use the other ring, before re-equipping the CE ring. Thing is you have to code in the ring names yourself. If you wanted it to work with any two rings the MWSE code is pretty hairy.

it is not exactly what you want, but I made a mod named http://oblivionmodgods.de/mrmuhs-macros-morrowind-t484.html with which you can define a set of equipped items which can be re-equipped by hotkey.