The Red Cap is a mid-ranked light armor headgear in Final Fantasy XII that boosts the wearer's magickal defense by 19 (Zodiac) or 18 (original), HP by 150, and Vitality by 3. It can thus seem a good headgear for those who use weapons that take the wielder's Vitality stat into account: axes and hammers and hand-bombs. However, a helm that boosts Strength has a bigger impact on the damage dealt, and in the Zodiac versions, the Foebreaker can't natively equip light armor.
It is found in a treasure on the Ozmone Plain's The Shred (the side where the entrance to the Henne Mines is; 50% chance to appear, 40% chance for gil, 50% chance the item treasure is the Red Cap without the Diamond Armlet equipped). It very rarely drops from the Hellhound.
The Red Cap is made in the bazaar set "Matching Reds" by selling three Coeurl Pelts (from Coeurls), two Quality Hides (from various enemies, e.g. Viper), and three Dark Magicites (from various enemies, e.g. Black Chocobo).
In the updated Zodiac versions, the Red Cap is sold for 2,500 gil in Eruyt Village and Mt Bur-Omisace. It is found in a treasure in Golmore Jungle's The Needlebrake (75% chance to appear, 45% chance for gil, 50% chance the item treasure is the Red Cap without the Diamond Armlet equipped), and Paramina Rift's Head of the Silverflow (70% chance to appear, 35% chance for gil, 50% chance the item treasure is the Red Cap without the Diamond Armlet equipped), as well as in Trial Mode Stage 60 with the Diamond Armlet equipped.
It still very rarely drops from the Hellhound and is made in the bazaar set "Matching Reds" with the same items as before.
The Red Cap is a mid-ranked light armor hat, giving 18 or 19 magick resist depending on version, and 150 HP, as well as 3 Vitality. It is useful to equip over any inferior equipment the party may have. However, in the original version where everyone can wear any equipment piece, the more expensive heavy armor helm, Golden Helm, or the mystic hat Feathered Cap, may be preferable purchases if the player can stretch their funds to them, as the HP boost from light armor is not usually worth prioritizing over heavy armor that boosts Strength for physical attackers, or mystic armor that boosts Magick Power for spellcasters. Though the Red Cap boosts Vitality, its effect is small, and even those whose weapons take the wielder's Vitality stat into account benefit more from the Strength-boosting heavy armor helms.
In the Zodiac versions, Machinist, Monk, Archer, and Shikari can equip the Red Cap, and so it is only useful to buy if the player has chosen these License Boards for their party. In The Zodiac Age, after fighting Belias, the player can choose two License Boards per party member, and so more party members can choose from the potentially more useful heavy and mystic armor sets. None of these jobs' base weapons also benefit from the Vitality boost the Red Cap offers, though the Machinist can access mid to late-game hand-bombs by unlocking Shemhazai and Zeromus; the Machinist will likely do more damage with guns, however, and these late-game Espers are more useful when assigned to other boards.