In pathfinder, a Wizard's bonded item can only be an amulet, ring, wand, or staff. Why? Is there something gamebreaking about allowing a head-slot item as a bonded item? We're considering removing the rule but we're not sure why it was there in the first place.
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Deciding on the Appropriateness of a Bonded Item
What's the nature of a amulet, ring, wand, staff, or weapon (the current RAW bonded item types)?
They're obviously arcane doodads and can be easily stolen, esp. by a steal or disarm combat maneuver. All of them suffer from the likelihood of eventual upgrade (you run through wand charges, outgrow that +1 amulet or low-level ring, and don't get magical staves till high level).
A jeweled headband or the like fits both those criteria. It's as stealable as a ring for sure.
Wizards are likely to have a headband slot item (intellect stat boost) but they're likely to have those other slots filled too - there's no real slot-related balance reason, especially because the bonded-ness doesn't really affect the functioning of the item per se. You're likely to need to upgrade it at the same cadence as an amulet. You can start upgrading it at level 3 (Craft Wondrous Item), earlier than some other types but same as amulets. I see zero difference between a headband and an amulet rule-wise.
Conversely, "my armor," "my socks," or "something slotless concealed in my colon," or similar are bad allowed bonded items because they lack the obviousness and stealability criteria.
Now, the character will benefit from having a nonstandard bonded item slot (the cops/their captors know "hey take wands, staves, amulets, weapons, and rings off captured wizards") so it would be fair to make them spend a trait on this change.
Note that the Hellknight Signifer prestige class gets an "Enforcer Mask" which is their arcane bonded item and it's a head slot item, so there is definitely precedent. This falls under the category of "well known" so it's also easy for a captor to deprive them of. If the PC is part of some group with a similarly well known alternate arcane bond location then that would work without a trait spend IMO.
A bonded item is what a Wizard channels his special spell through. Although doubtful it would be game breaking, bonding a helm would mean that for the purposes of role play, whenever you cast the spell, you'd point the top of your head at the target.
Hilarity would ensue as you'd probably miss whilst looking at the floor..
Hence why you can bond
They can all be "easily" stolen. Trying to steal a helm would be ridiculous
Bonded items are in locations that can be non-fatally removed and can be easily pointed. The head is not such a location.