#This is not balanced
This is not balanced
The concern with this is that many characters who wear armor are on the front-line. Their job isn't to be perceptive, their job is to smash and stay alive. Trading away some perception for increased survivability becomes a no-brainer. And anything that's a "definitely yes" decision tree is unlikely to be balanced.
AC vs Perception
##AC vs Perception WhetherWhether or not skill checks are used in combat is going to be very DM dependent. Looking at this from a purely mechanical perspective, AC is always on. Skill checks are dependent upon the DM and on the table. Player roles also start to become involved. If someone has built a character for combat and is willing to let softer skills suffer (not an uncommon decision), then this becomes a very clear decision. Especially if other party members pick up the slack on the skills side.
But if your table utilizes perception and other skills more frequently, and more specifically in combat, then the trade-off becomes more interesting as they'll have to decide if it's 'worth it'. But at that point, as other answers have suggested, moving this to an action cost for don/doffing also becomes necessary.
##Equivalence/relationship to existing magical items
Equivalence/relationship to existing magical items
+1 Armor
###+1 Armor ThisThis is basically an option to turn on/off a +1 to armor. +1 armor is itself a rare item, so if you were to offer this, it should be treated like a rare magic item, but providing a cost for donning/doffing should also be a consideration. However, it's important to note that you can wear this and have it stack with the armor, which increases it's value/rarity when doing so.
Bracers of Defense
##Bracers of Defense TheThe Bracers provide a +2 AC, but have the limitation of no armor or shield being used. It's a standalone item that can't be combined with armor, but is still rated as Rare.