+1 AC for a perception penalty is a fair trade.
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Investigation is not commonly used, and susceptibility to flanking would add a whole new system. The exhaustion ticking is too easy to counter and difficult to track.

Perception is useful and important
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However, perception is extremely important both in and out of combat. Being forced to take a penalty on perception would mean that donning a helm is a choice with advantages and disadvantages. Even during combat it may be better to remove your helm to locate a hiding foe, or listen for approaching foes. 

Use disadvantage instead of a penalty
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Having modifiers to abilities isn't common though. Usually 5e relies on disadvantage. 

Consider the action economy penalty
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Out of combat you probably want to take your helm off so you can keep your perception at a reasonable level. You may even want to stow your helm so you have a hand free to use a torch, interact with switches and other objects, or whatever else.

When it's time to fight you will have to get your helm back on your head. If it is in your hand, that requires the free object interaction for the turn. If you stowed it, then it takes free object interaction to unstow it, and then an action to put it on your head.

This could have a big impact on action economy and the way that your character behaves out of the fight. Normally you would draw your weapon with object interaction, and then attack (or cast a spell, etc) with your action. However if you use your object interaction when putting on the helm, then you will need to use your action to pull out your weapon. Worse still, if your helm was in your pack, you will have to wait until turn 2 to even draw your weapon.

If, during the fight, you need to take off the helm to locate a hiding foe, or listen for extra monsters that may join the fight, then you need to use your object interaction, and you need to have a free hand.

Suggested stats
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You could implement a simple helm that seems balanced like so:

>**Helmet**
>
>While wearing a helmet, you gain a +1 bonus to AC, but you have disadvantage on Wisdom (Perception) checks that rely on sight or hearing.

What if you aren't playing much of anything other than combat?
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However, if you are playing a hack 'n' slash style game that is purely straight up meat-grinder combat where perception is not used, and you can walk around with your helm in one hand and your sword in the other, then it's a no-brainer +1 AC.

No-brainers are generally bad. Using your brain is fun!

I go into more detail [here][1].

  [1]: https://rpg.stackexchange.com/a/160858/59609